designers guide to en 1991-1-2, en 1992-1-2, en 1993-1-2 and en 1994-1-2 handbook for the fire...

Designers’ guide to EN1991-1-2, EN1992-1-2, EN1993-1-2

and EN1994-1-2T. Lennon, D. B. Moore, Y. C. Wang and C. G. Bailey

Series editor Haig Gulvanessian

This series of Designers’ Guides to the Eurocodes provides comprehensive guidance in the form of design aids, indications for the most convenient design procedures and worked examples. The books also include background information to aid the designer in understanding the reasoning behind and the objectives of the code. All individual guides work in conjunction with the Designers’ Guide to EN1990 Eurocode: Basis of structural design.

Designers’ Guide to EN1991-1-2, EN1992-1-2, EN1993-1-2 and EN1994-1-2 differs from the other Eurocode guides available in that it is not concerned with a single design standard. The UK standard for the design of steel structures encompasses the rules for both structural steelwork and for composite steel and concrete construction. The fire design procedures for reinforced and prestressed concrete structures are contained in the relevant part of the National code. However, the structural Eurocodes consider steel, composite and concrete construction in isolation and each material therefore has its own corresponding fire part.

The design methodology, as set out in the fire parts of the structural Eurocodes, is based on the principles adopted for normal temperature design. One of the aims of this book is to demystify the subject so that it can be readily understood and used by structural engineers used to the underlying principles and assumptions of design for the ambient condition. This present Designers’ Guide provides guidance on the nature of the loading that must first be understood before applying the structural engineering principles set out in the Eurocodes. For this reason the book is meant as a guide to four separate documents EN1991-1-2, EN1992-1-2, EN1993-1-2 and EN1994-1-2 with reference, where appropriate, to the Eurocode covering basis of design.

This guide is essential reading for:

■ civil and structural engineers■ code-drafting committees■ clients■ structural-design students■ public authorities

in fact, everyone who will be affected by the Eurocodes.

Tom Lennon has worked at the British Research Establishment for over 20 years. He was responsible for the programme of full-scale fire tests carried out at BRE’s large-scale test facility at Cardington on steel, concrete and timber framed buildings. Mr Lennon has extensive experience of the Structural Eurocodes. He is a prominent member of British Standards committee B525/-/32 the mirror group for the fire part of EC1 responsible for the implementation of the code in the UK. Mr Lennon is a member of the project team responsible for developing the draft National Annex for use with EN 1991-1-2. He is author of a number of papers, design guides and journal articles on the subject of structural fire engineering design.

Dr David B. Moore is the Director of Engineering at the British Constructional Steelwork Association and has over 25 years experience of research and specialist advisory work in the area of structural engineering and he has published over 50 technical papers on a wide range of subjects many of them in international journals. He has also made a significant contribution to a number of specialised design guides and best practice guides for the steel industry. Many of these publications are used daily by practising structural engineers and steelwork fabricators.

Dr Yong C. Wang teaches fire engineering at the University of Manchester and has been engaged in research on fire resistance of steel and composite structures for a number of years. He was Senior Research Engineer at the Building Research Establishment and was a member of the working group responsible for the amendment of BS5950 Part 8. He is the author of Steel and composite structures – behaviour and design for fire safety.

Colin G. Bailey is currently Professor of Structural Engineering at the University of Manchester. He has previously worked for the design consultants Lovell Construction, Cameron Taylor Bedford and Clarke Nicholls Marcel, where he designed and supervised the construction of a number of concrete, steel and masonry structures. He has also worked for The Steel Construction Institute and The Building Research Establishment, where his practical and research experience resulted in significant developments in structural engineering design. His main specialties are fire safety engineering of structures, membrane action, wind loading, and steel–concrete composite systems.

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DESIGNERS’ GUIDES TO THE EUROCODES

DESIGNERS’ GUIDE TO EN 1991-1-2, 1992-1-2,1993-1-2 and 1994-1-2

HANDBOOK FOR THE FIRE DESIGNOF STEEL, COMPOSITE AND CONCRETESTRUCTURES TO THE EUROCODES


Eurocode Designers’ Guide SeriesDesigners’ Guide to EN 1990. Eurocode: Basis of Structural Design. H. Gulvanessian, J.-A. Calgaro andM. Holicky. 0 7277 3011 8. Published 2002.

Designers’ Guide to EN 1994-1-1. Eurocode 4: Design of Composite Steel and Concrete Structures. Part 1.1:General Rules and Rules for Buildings. R. P. Johnson and D. Anderson. 0 7277 3151 3. Published 2004.

Designers’ Guide to EN 1997-1. Eurocode 7: Geotechnical Design – General Rules. R. Frank, C. Bauduin,R. Driscoll, M. Kavvadas, N. Krebs Ovesen, T. Orr and B. Schuppener. 0 7277 3154 8. Published 2004.

Designers’ Guide to EN 1993-1-1. Eurocode 3: Design of Steel Structures. General Rules and Rules for Buildings.L. Gardner and D. Nethercot. 0 7277 3163 7. Published 2004.

Designers’ Guide to EN 1992-1-1 and EN 1992-1-2. Eurocode 2: Design of Concrete Structures. General Rulesand Rules for Buildings and Structural Fire Design. A. W. Beeby and R. S. Narayanan. 0 7277 3105 X. Published2005.

Designers’ Guide to EN 1998-1 and EN 1998-5. Eurocode 8: Design of Structures for Earthquake Resistance.General Rules, Seismic Actions, Design Rules for Buildings, Foundations and Retaining Structures. M. Fardis,E. Carvalho, A. Elnashai, E. Faccioli, P. Pinto and A. Plumier. 0 7277 3348 6. Published 2005.

Designers’ Guide to EN 1995-1-1. Eurocode 5: Design of Timber Structures. Common Rules and for Rules andBuildings. C. Mettem. 0 7277 3162 9. Forthcoming: 2007 (provisional).

Designers’ Guide to EN 1991-4. Eurocode 1: Actions on Structures. Wind Actions. N. Cook. 0 7277 3152 1.Forthcoming: 2007 (provisional).

Designers’ Guide to EN 1996. Eurocode 6: Part 1.1: Design of Masonry Structures. J. Morton. 0 7277 3155 6.Forthcoming: 2007 (provisional).

Designers’ Guide to EN 1991-1-2, 1992-1-2, 1993-1-2 and EN 1994-1-2. Eurocode 1: Actions on Structures.Eurocode 3: Design of Steel Structures. Eurocode 4: Design of Composite Steel and Concrete Structures. FireEngineering (Actions on Steel and Composite Structures). Y. Wang, C. Bailey, T. Lennon and D. Moore.0 7277 3157 2. Forthcoming: 2007 (provisional).

Designers’ Guide to EN 1992-2. Eurocode 2: Design of Concrete Structures. Bridges. D. Smith and C. Hendy.0 7277 3159 9. Forthcoming: 2007 (provisional).

Designers’ Guide to EN 1993-2. Eurocode 3: Design of Steel Structures. Bridges. C. Murphy and C. Hendy.0 7277 3160 2. Forthcoming: 2007 (provisional).

Designers’ Guide to EN 1991-2, 1991-1-1, 1991-1-3 and 1991-1-5 to 1-7. Eurocode 1: Actions on Structures.Traffic Loads and Other Actions on Bridges. J.-A. Calgaro, M. Tschumi, H. Gulvanessian and N. Shetty.0 7277 3156 4. Forthcoming: 2007 (provisional).

Designers’ Guide to EN 1991-1-1, EN 1991-1-3 and 1991-1-5 to 1-7. Eurocode 1: Actions on Structures. GeneralRules and Actions on Buildings (not Wind). H. Gulvanessian, J.-A. Calgaro, P. Formichi and G. Harding.0 7277 3158 0. Forthcoming: 2007 (provisional).

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DESIGNERS’ GUIDES TO THE EUROCODES

DESIGNERS’ GUIDE TO EN 1991-1-2, 1992-1-2,1993-1-2 and 1994-1-2

HANDBOOK FOR THE FIRE DESIGNOF STEEL, COMPOSITE AND CONCRETESTRUCTURES TO THE EUROCODES

T. LENNON, D. B. MOORE, Y. C. WANG and C. G. BAILEY

Series editorH. GULVANESSIAN


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Preface

Many structural engineers will be unfamiliar with the principles of structural fire engineeringdesign. In recent years a number of specialist consultants have emerged offering fire engineer-ing solutions, largely for prestigious projects where the potential benefits of adopting a fireengineering design approach outweigh the additional design cost to the client. There is afundamental lack of understanding of the principles of structural fire engineering design.In reality the design methodology, as set out in the fire parts of the structural Eurocodes,is based on the principles adopted for normal temperature design. One of the aims of thisbook is to demystify the subject so that it can be readily understood and used by structuralengineers used to the underlying principles and assumptions of design for the ambientcondition.

This book differs from many of the other Eurocode guides available in that it is notconcerned with a single design standard. The UK standard for the design of steel structuresencompasses the rules for both structural steelwork and for composite steel and concreteconstruction. The fire design procedures for reinforced and prestressed concrete structuresare contained in the relevant part of the National Code. However, the structural Eurocodesconsider steel, composite and concrete construction in isolation and each material thereforehas its own corresponding fire part. In this case a clause-by-clause examination of thematerial codes would not be sufficient to allow designers to use these documents. Thenature of the loading must first be understood before applying the structural engineeringprinciples set out in the Eurocodes. For this reason the book is meant as a guide to fourseparate documents – EN 1991-1-2, EN 1992-1-2, EN 1993-1-2 and EN 1994-1-2 – withreference where appropriate to the Eurocode covering basis of design.


Contents

Preface v

Chapter 1. Introduction 1

1.1. Introduction to this handbook 11.2. Introduction to structural fire design 11.3. Scope of EN 1991 Part 1.2, EN 1992 Part 1.2, EN 1993 Part 1.2

and EN 1994 Part 1.2 41.4. Distinction between principles and application rules 51.5. National annexes and Nationally Determined Parameters 51.6. Definitions and symbols 8

Chapter 2. Design methods 13

2.1. Introduction 132.2. Design of concrete structures to EN 1992-1-2 162.3. Design of steel structures to EN 1993-1-2 162.4. Design of composite structures to EN 1994-1-2 172.5. Design assisted by testing 18

Chapter 3. Design fires 19

3.1. Introduction 193.2. General rules for calculating atmosphere temperatures 193.3. Nominal temperature–time curves 20

3.3.1. Standard temperature–time curve 203.3.2. External fire curve 203.3.3. Hydrocarbon curve 20

3.4. Equivalent time of fire exposure 213.5. Parametric temperature–time curves 233.6. External atmosphere temperature 263.7. Advanced fire models 26

Chapter 4. Member temperatures 27

4.1. Introduction 274.2. Section factors for steel and composite construction 274.3. Unprotected steelwork 274.4. Steelwork insulated by fire protection 284.5. Unprotected composite slabs 30


4.5.1. Steel decking 304.5.2. Reinforcement bars 314.5.3. Concrete slab over steel decking 32

4.6. Temperature profile for concrete members 33

Chapter 5. Static loads 35

5.1. Introduction 355.2. Partial safety factors for loads 355.3. Design values of loads 36

5.3.1. Loading 375.3.2. Ambient temperature design loads 375.3.3. Fire limit state design loads 375.3.4. Design values of actions – ultimate limit state accidentaldesign situation 37

5.4. Definition of load level, load intensity and degree of utilization 375.4.1. Load level (n) 375.4.2. Degree of utilization (�fi) 38

Chapter 6. Thermal and mechanical properties of materials 39

6.1. Introduction 396.2. Steel 39

6.2.1. Hot-rolled carbon steel 396.2.2. Stainless steel 436.2.3. Light-gauge steel 47

6.3. Concrete 486.3.1. Normal-weight concrete 486.3.2. Lightweight concrete 526.3.3. High-strength concrete 53

6.4. Reinforcing steel 546.5. Bolts and welds 55

Chapter 7. Design of tension members 57

7.1. Introduction 577.2. Design resistance method 57

7.2.1. Non-uniform temperature distribution 587.2.2. Uniform temperature distribution 60

7.3. Critical temperature method 60

Chapter 8. Design of compression members 63

8.1. Introduction 638.2. Effective length of columns in fire 648.3. Axially loaded steel columns 64

8.3.1. Uniformly heated column with class 1, 2 or 3cross-section 65

8.3.2. Uniformly heated column with class 4 cross-section 678.3.3. Uniformly heated column with combined axial load and

bending moment 678.3.4. Non-uniformly heated steel columns 67

8.4. Axially loaded composite column 678.4.1. General design method 688.4.2. Alternative design method for composite column with

partially encased steel section 71

DESIGNERS’ GUIDE TO EN 1991-1-2, 1992-1-2, 1993-1-2 AND 1994-1-2

viii


8.4.3. Alternative design method for composite columns withconcrete-filled hollow sections 78

8.5. Reinforced concrete columns 798.5.1. 50088C isotherm method 808.5.2. Zone method 808.5.3. Additional comments 81

Chapter 9. Design of bending members 83

9.1. Introduction 839.2. Steel beams 83

9.2.1. Bending moment capacity 839.2.2. Shear resistance 859.2.3. Lateral torsional buckling 869.2.4. Control of deformation 86

9.3. Steel beam exposed to fire on three sides with concrete slab onthe fourth side 87

9.4. Composite beams comprising steel beams with partial concreteencasement 88

9.5. Reinforced concrete beam 919.6. Comments on EN 1992-1-2 tabulated data 92

Chapter 10. Design of slabs 93

10.1. Introduction 9310.2. Composite slabs 9310.3. Reinforced concrete slabs 101

Chapter 11. Other forms of construction 103

11.1. Introduction 10311.2. Slim floor beams 10311.3. Shelf angle beams 10311.4. Blocked infilled columns 106

Chapter 12. Connections 109

12.1. Introduction 10912.2. Concrete connections 109

12.2.1. Increase in support moment for continuous structures 11012.2.2. Forces due to restrained thermal expansion 11012.2.3. Eccentricity of loading due to large deflection 110

12.3. Steel and composite connections 111

Chapter 13. General discussion 121

13.1. Introduction 12113.2. Guidance on selection of appropriate design method 121

References 123

Index 127

ix

CONTENTS


CHAPTER 1

Introduction

1.1. Introduction to this handbookIn writing this handbook the authors have been aware that many designers will be unfamiliarwith the principles of structural fire engineering design. In recent years a number of specialistconsultants have emerged offering fire engineering solutions largely for prestigious projectswhere the potential benefits of adopting a fire engineering design approach outweigh theadditional design cost to the client. The subject is shrouded in mystery and is viewed bymany engineers as a black art. One of the aims of this book is to demystify the subject sothat it can be readily understood and used by civil and structural engineers familiar withthe underlying principles and assumptions of design for the ambient condition.

This book differs frommany other Eurocode guides in that it is not concerned with a singledesign standard. The UK standard for the design of steel structures encompasses the designrules for both structural steelwork and for composite steel and concrete construction, albeitin different parts.1�3 The fire design procedures for reinforced and prestressed concretestructures are contained in the relevant parts of the national code, BS 8110.4;5 However,the structural Eurocodes consider steel, composite and concrete construction in isolationand each material therefore has its own corresponding fire part. In this case a clause-by-clause examination of the fire parts of the material codes would not be sufficient to allowdesigners to use these documents. The nature of the loading must first be understoodbefore applying the structural engineering principles set out in the Eurocodes. For thisreason this book is meant as a guide to four separate documents, namely EN 1991 Part1.2, EN 1992 Part 1.2, EN 1993 Part 1.2 and EN 1994 Part 1.2, with reference whereappropriate to the Eurocode covering the basis of design, namely EN 1990.6

The guide will take the form of an introduction to the procedures required to achievedesign solutions for a typical range of structural elements and assemblies. Worked exampleswill be included along with the text where appropriate to illustrate the use of the Eurocodesfor specific design scenarios. As a way of setting the scene for those unfamiliar with the basicprinciples of structural fire engineering design, the next section provides an overview ofthe regulatory framework and a description of the commonly used methods for ensuringcompliance with the regulations in the UK.

1.2. Introduction to structural fire designIn the UK the fire resistance requirements for buildings are specified in the Building Regula-tions for England and Wales7 with regional differences covered in separate documents forconstruction in Scotland8 and Northern Ireland.9 All buildings must meet certain functionalrequirements covering means of escape, internal fire spread, external fire spread and accessand facilities for the Fire Service as laid down in the regulations. It is important to note thatthe Building Regulations are only intended to ensure reasonable standards of health and


safety for those in and around the building. They are not designed to limit structural damageother than to achieve this aim and they are not designed to minimize financial losses arisingfrom a fire. This has important implications for the fire engineering design of buildings wherethe requirements of the regulations may not be sufficient to meet the needs of the client.

For present purposes the most important requirement is that dealing with internal firespread as related to structural elements which states:7

The building shall be designed and constructed so that, in the event of a fire, its stability willbe maintained for a reasonable period.

The Approved Document provides detailed guidance on ways to demonstrate compliancewith the functional requirements. However, it is important to emphasize that it is the require-ment which is mandatory NOT the guidance. This allows for alternative approaches tomeeting the requirements, which can be developed in collaboration with the regulatoryauthorities. In general, the most common route to demonstrate compliance has been tofollow the guidance in the ApprovedDocument. The development of the Eurocodes providesfor alternative methods for satisfying the regulatory requirement through performance-based calculation.

For steel and concrete members both strength and stiffness decrease with increasing tem-perature and this reduction is particularly significant between 4008C and 7008C. The mostcommon method of ‘designing’ steel structures for the fire condition is to design the buildingfor the ambient temperature loading condition and then to cover the steel members with pro-prietary fire protection materials to ensure that a specific temperature is not exceeded or, putanother way, that a specified percentage of the ambient temperature loading capacity ismaintained. For concrete structures the required performance in fire is usually achievedby reference to tabulated values for minimum dimensions and minimum cover to thereinforcement.10 For concrete structures the dimensions adopted for the ambient tempera-ture condition and for durability will often be sufficient to achieve the required fire resistance.

The requirement for the building to maintain stability for a reasonable period hastraditionally been related to a required time for survival in a standard fire test. The detaileddrawbacks and advantages of the standard test are discussed in Section 3.3 of this handbook.The fire resistance requirements contained in the guidance to the Approved Document relatedirectly to fire resistance time and it is often incorrectly assumed that there is a one-to-onerelationship between survival in a fire resistance test and survival in a fire. This is clearlynot the case. Real fires may be more or less severe (either in the time or temperaturedomain) than the standard fire curve, depending on the particular characteristics of thefire enclosure. The traditional design criterion is that the fire resistance is greater than thetime required by the regulations based on the assessment of the building as belonging to aparticular purpose group. Fire resistance is defined relative to three failure criteria:insulation, integrity and load-bearing capacity. These terms are explained in greater detailin Chapter 3. This is the method by which the vast majority of buildings are designed.The prescriptive nature of the regulations has hindered the development of a more rationalapproach to the design of buildings for fire.

As mentioned above, the traditional means of achieving specified periods of fire resistancefor steel-framed buildings is to apply passive fire protection to the structural elements. Thispassive fire protection may be in the form of traditional construction materials such asconcrete or brickwork. Up until the late 1970s, concrete was the most common form offire protection for structural steelwork. However, the high cost of this form of protectiontogether with the problem of spalling in fires led to the development of alternativemethods. More frequently, insulation is provided by spray or board fire protection orsome combination of the two. Intumescent coatings may be preferred to the more traditionalmethods. Sprayed systems are popular where the steelwork is not visible, such as floor soffitshidden by a suspended ceiling. Board protection is preferred where the protection is to be leftexposed. In modern steel-framed offices the most common form of protection is to spray thebeams and to protect the columns with boards. A useful source of information on commonlyused fire protection materials is ‘The Yellow Book’11 published jointly by the Association for

2



Specialist Fire Protection and the Steel Construction Institute (SCI). The Yellow Bookprovides information on the thickness of protection for specified periods of fire resistance.

A major change in the design methodology for steel structures in fire came about with thepublication in 1990 of BS 5950 Part 812 (subsequently revised in 200313). Although this codeis still based on an evaluation of the performance of structural steel and composite membersin the standard fire test, it allows architects and engineers an alternative approach ofdesigning for fire resistance by calculation. Unlike the Approved Document, the code is con-cerned only with restricting the spread of fire and minimizing the risk of structural collapse.It recognizes that there is no single ‘failure temperature’ for steel members and that structuralfailure is influenced not only by temperature but also by load level, support conditions andthe presence or otherwise of a thermal gradient through and/or along the member. The codeallows for consideration of natural fires but does not provide any detailed information orguidance. Load factors and material strength factors specific to the fire limit state aregiven. These are partial safety factors which deal with the uncertainties inherent in probabil-istic distributions for loading and material properties and represent reductions from ambienttemperature design in recognition of the small probability of excessive loads being present atthe same time as a fire occurs.

The most common method of achieving the specified fire resistance for steel structuresremains the application of passive fire protection. The thickness of fire protection isderived from a consideration of the Section Factor (Hp=A or Am=V). This is the ratio ofthe heated perimeter to the gross cross-sectional area to allow for the varying rates atwhich different steel sections heat up during a fire. The thickness of fire protection is thenselected by reference to The Yellow Book for specified periods of fire resistance andsection factors or, alternatively, calculated according to the formula given in Appendix Dof BS 5950 Part 8.13

Calculation methods included in BS 5950 Part 8 include the limiting temperature method.This simple but effective procedure uses the concept of load ratio – that is, the ratio of theload carried during the fire to the ambient temperature load capacity – to derive a limitingtemperature, which is then compared with the design temperature to assess the need forpassive protection. The design temperature may be determined either from tests or fromtabulated data published in the code. A reduction in this value is allowed for I or H sectionswith low aspect (D=B) ratios to account for shielding effects. It should be borne in mind thatthe limiting temperature method is not applicable to beams with high shear load. Thismethod utilizes the reduced load factors for the fire limit state.

An alternative option is to use the moment capacity method. This method cannot be usedfor slender sections. It is not widely used, as knowledge of the temperature profile of thebeam is required. The moment capacity is based on the known temperature of the criticalelement with the relevant strength reduction factor used. If the moment capacity does notexceed that applied at the fire limit state then the beam does not require protection.

Composite slabs are included in the code through the use of simple look-up tables for thecritical dimensions and temperature data, which can be incorporated in a more extensive fireengineering analysis. A useful flow chart is included in the original version of the code,summarizing the options and procedures available; however, this was removed from the2003 revision.

The SCI has produced an informative handbook14 to be used in conjunction with the code.This includes tabulated values of section factors for commonly used sections and methods ofprotection as well as separate chapters dealing with the limiting temperature and momentcapacity methods of calculation. It also provides design examples to illustrate the use ofthe code.

The fire provisions for concrete structures are contained in BS 8110 Part 25 and are basedon the results from standard tests.15 The current code provisions in BS 8110 refer to datapublished in Guidelines for the Construction of Fire Resisting Structural Elements10 andinclude variation in requirements depending on whether normal-weight or lightweightconcrete is used and, for beams and floors, a recognition of the beneficial aspects of continu-ity on fire resistance. The tabulated provisions for minimum dimensions and minimum cover

3

CHAPTER 1. INTRODUCTION


are based around the need to limit the temperature rise on the unexposed face and tomaintain stability for a reasonable period. This is achieved by providing a sufficient depthof concrete to limit the temperature rise on the unexposed face to a mean temperature of1408C and sufficient cover to limit the temperature rise of the reinforcement to 5508C(4508C for prestressing tendons). In general these provisions have proved to provide anacceptable level of safety based on experience of real fires. The development of the structuralEurocodes has provided an opportunity for UK designers to adopt a performance-basedapproach to designing concrete structures for the effects of real fires, taking into accountthe beneficial aspects of whole-building behaviour and the inherent continuity and robust-ness of properly detailed concrete buildings.

The fire parts of the Eurocode set out a new way of approaching structural fire design. Toengineers familiar with BS 5950 Part 8, the design procedures in EN 1993-1-2 will berelatively familiar. However, for concrete designers more familiar with a very simpleprescriptive approach to the design of structures for fire, based on the use of simple look-up tables, the new philosophy may appear unduly complex. However, the fire designmethodology in the Eurocodes affords designers much greater flexibility in their approachto the subject. The options available range from a simple consideration of isolatedmember behaviour subject to a standard fire, to a consideration of the physical parametersinfluencing fire development coupled with an analysis of the entire building. The availableoptions are discussed in more detail in Chapter 2. This rather complex process can effectivelybe simplified into a three-phase procedure consisting of the characterization of the firemodel, a consideration of the temperature distribution within the structure and an assess-ment of the structural response to the fire. What is different about the European system isthat all the information required by the designer is no longer available within a single docu-ment. Information on thermal actions for temperature analysis is taken from EN 1991-1-2;the method used to calculate the temperature rise of structural steelwork (either protected orunprotected) is found in EN 1993-1-2 and EN 1994-1-2; values for the temperature ofconcrete members subject to a standard fire exposure are tabulated in EN 1992-1-2. Thedesign procedures to establish structural resistance are set out in the fire parts of EN 1992,EN 1993 and EN 1994 but the actions (or loads) to be used for the assessment are taken fromthe relevant parts of EN 1991. The simplified procedure and the relationship between thevarious European Standards is explained in Chapter 2.

1.3. Scope of EN 1991 Part 1.2, EN 1992 Part 1.2, EN 1993Part 1.2 and EN 1994 Part 1.2EN 1991-1-216 is the fire part of Eurocode 1. It is intended for use in conjunction with the firedesign parts of Eurocodes 2 to 9, which are concerned with design for various materials andspecial circumstances. A more detailed description of the nature and extent of the structuralEurocodes may be found in an earlier book in this series.17 EN 1991 Part 1.2 provides generalprinciples and actions for the structural design of buildings and civil engineering works and isonly valid if the ambient temperature design is carried out in accordance with the relevantstructural Eurocodes.

The temperature–time curves (thermal actions in the code) used for structural analysismay be either nominal or physically based fire models. Typical nominal curves wouldinclude the ‘standard’ time–temperature response (ISO 834,18 BS 476 Part 20,19 BSEN 1363-120) used to determine fire resistance or the more severe hydrocarbon curve usedby the offshore and petroleum industries among others. More information is provided inChapter 3 Section 3.3. Physically based natural fire models include the parametric approach,time equivalent method and advanced calculations such as zone or field models. Moreinformation is given in Chapter 3.

The fire part of the structural Eurocode for the design of steel structures, EN 1993 Part1.2,21 in common with BS 5950 Part 8, contains information on steel properties at elevatedtemperature for use in calculation models to determine resistance at elevated temperature.

4



However, there are a number of significant differences between the European and Nationaldocuments.

EN 1993 Part 1.2 is not a stand-alone document. In relation to the calculation of the time–temperature response, the code is designed to be used in conjunction with the fire part ofEurocode 1. The fire part of EN 1993 deals with the design of steel structures for the acciden-tal situation of fire exposure with particular reference to the load-bearing function and onlyidentifies differences from, or supplements to, normal temperature design. It is concernedonly with passive (as opposed to active) forms of fire protection. Cold-formed membersare also covered by the fire part of EN 1993. Composite construction is not dealt withhere but in the corresponding fire part of the composite code, EN 1994. There is a changein emphasis from UK practice in that design by calculation is acknowledged as the preferredapproach, with design based on the results from tests presented as an alternative option.

The fire part of the Eurocode for composite steel and concrete structures, EN 1994-1-2,22 issimilar in scope to the corresponding part of the steel code. Material properties at elevatedtemperature are given for structural steel, reinforcing steel and concrete (see Chapter 6).Tabular data are presented for cross-sectional dimensions and area of reinforcement for arange of composite beams and columns. The use of the tabulated data is restricted to thestandard fire exposure.

The fire part of the Eurocode for concrete structures, EN 1992 Part 1.2,23 deals with thedesign of concrete structures for the accidental situation of fire exposure and is intendedto be used in conjunction with the main part of EN 199224 and the fire part of the Eurocodefor Actions.16 It deals with the avoidance of premature collapse of the structure and the limit-ing of fire spread beyond the compartment of origin. Design methods and tabulated data areprovided for reinforced and prestressed concrete columns, walls (load-bearing and non-load-bearing), tension members, reinforced and prestressed beams, and reinforced and prestressedslabs. EN 1992 Part 1.2 does not cover structures with prestressing by external tendons, shellstructures and active fire protection. The fire design standard provides data on materialproperties at elevated temperature of concrete (normal strength, lightweight and highstrength), reinforcing steel and prestressing steel (see Chapter 6). It is important to notethat the thermal conductivity for concrete specified in this document differs from the corre-sponding value in EN 1994. The reasons for this are explained in Chapter 6.

1.4. Distinction between principles and application rulesIn common with all Eurocodes, the four documents described above make a distinctionbetween principles and application rules. The principles are general statements and defini-tions for which there is no alternative. Application rules are generally accepted methods,which follow the principles and satisfy their requirements. It is permissible to use alternativesto the application rules but the designer must demonstrate that the chosen alternative alsosatisfies the principles with at least the same degree of reliability.

To take an analogy with a document likely to be familiar to readers of this handbook,principles may be compared to the functional requirements of Approved Document B.Application rules could then be viewed in the same light as the prescriptive guidanceprovided on meeting the requirements. It is possible for designers to develop alternativeperformance-based solutions to meet the functional requirements but such alternativesmust be shown to be at least as reliable as the prescriptive solution. Procedures in current

national codes will, in many cases, satisfy the principles in the Eurocodes.

1.5. National annexes and Nationally Determined ParametersThe National standards implementing the Eurocodes will comprise the full text of theEurocode (including any technical annexes), as published by CEN preceded by a Nationaltitle page and National Foreword followed by a National Annex (NA). The NA onlycontains information on those parameters which are left open in the Eurocode for national

5



choice, known as Nationally Determined Parameters (NDPs), to be used for the design ofbuildings and civil engineering works to be constructed in the country concerned. A list ofthe clauses for which national choice is permitted together with the recommended valuefrom the Eurocode and the NA value (where available) is given in Table 1.1 below. Forthose familiar with the ENV version of the Eurocodes, the National Annex is analogousto the National Application Document and the Nationally Determined Parameters to theboxed values.

Table 1.1. Summary of Nationally Determined Parameters. (Note: At the time of writing, many of theseissues have not been finalized. Readers are asked to consult the final National Annexes published by BSI)

Clause Description Recommended value National Annex value

EN 1991-1-2

2.4(4) Periods of fire resistance National regulations ofTechnical Annex F

National regulations and fireengineering approach

3.1(10) Choice of nominal or naturalfire models

Either nominal or natural firemodels

Either nominal or natural firemodels

3.3.1.1(1) Simple fire models –calculation of fire load density

Annex E for calculation of fireload density

Simple models allowed – fireload density from BS 7974PD125

3.3.1.2(1) Procedure for calculating theheating conditions for internalmembers in compartment fires

At least fire load density andventilation conditions

Use of parametric approach(Technical Annex A)permitted subject tocomplementary information

3.3.1.2(2) Procedures for calculating theheating condition for externalmembers in compartment fires

Use of Annex B Annex B allowed subject tocomplementary information

3.3.1.3(1) Procedure for calculating theheating condition where fireremains localized

Use of Annex C Alternative procedure in BS7974 PD1 to be used

3.3.2(1) Procedures for calculating fireload density and heat releaseusing advanced fire models

Calculation of fire load densityand heat release using Annex E

Fire load density and heatrelease from BS 7974

3.3.2(2) Selection of advanced firemodels

One-zone, two-zone orcomputational fluid dynamics(CFD) models to be used

One-zone, two-zone or CFDmodels to be used

4.2.2(2) Type of additional actions tobe considered

Choice of additional actions No additional actions to beconsidered

4.3.1(2) Combination rules for actions Quasi-permanent value 2;1

recommendedFrequent value 1;1 to be used

EN 1992-1-2

2.1.3(2) Temperature rise for decayphase

��1 ¼ 200K, ��2 ¼ 200 K No change

2.3(2) Partial factor �M;fi 1.0 thermal and mechanical forall materials

No change

3.2.3(5) Parameters for stress–strainrelationship of reinforcementat elevated temperature

Choice of Class N or Class X Class N

3.2.4(2) Parameters for the stress–strain relationship ofprestressing steel at elevatedtemperature

None Class A

6



Table 1.1. Continued


EN 1992-1-2 Continued

3.3.3(1) Thermal conductivity Value between upper andlower limit

Lower limit

4.1(1)P Use of advanced calculationmethods to satisfy 2.4.1(2)P

None Properly validated advancedcalculation methods may beused

4.5.1(2) Value of moisture content k%below which spalling is unlikelyto occur

3% No change

5.2(3) Reference load level for use oftabulated data �fi

0.7 No change

5.3.1(1) Tabulated data for unbracedstructures

None None given

5.3.2(2) Value of emax 0.15h (or b) No change

5.6.1(1) Web thickness Choice of Class WA, WB orWC

No change

5.7.3(2) Additional rules on rotationcapacity at supports forcontinuous solid slabs

— No additional rules

6.1(5) Reduction of strength atelevated temperature forhigh-strength concrete

For C55/67 and C60/75 Class 1of Table 6.1NFor C70/85 and C80/95 Class 2of Table 6.1NFor C90/105 Class 3 of Table6.1N

Normally the recommendedclasses should be used.Alternative values may be usedonly if satisfactory testevidence is available

6.2(2) Measures to control spalling ofhigh-strength concrete

Methods A, B, C and D Any single method orcombination of methods maybe used

6.3.1(1) Thermal conductivity forhigh-strength concrete

Within the limits given inclause 3.3.3

Upper limit

6.4.2.1(3) Value of factor k 1.1 for Class 1, 1.3 for Class 2 No change

6.4.2.2(2) Value of factor km Table 6.2N No change

EN 1993-1-2

2.3(1) Partial factor �M;fi formechanical properties

1.0 1.0

2.3(2) Partial factor �M;fi for thermalproperties

1.0 1.0

2.4.2(3) Reduction factor �fi 0.65 or 0.7 for category E —

4.1(2) Choice of design methods forfire resistance

Simplified, calculation,advanced calculation,testing

Any suitable design method ispermitted

4.2.3.6(1) Choice of criticaltemperature for Class 4sections �crit

3508C 3508C

4.2.4(2) Critical temperature forcarbon steel �a;cr

Formula in code Revised version ofTable 4.1 based on UKexperience

7



1.6. Definitions and symbolsA number of definitions are common to the four Eurocodes considered in this book. Themost important definitions together with the associated symbols and units where appropriateare summarized in Table 1.2 below. The terminology in the Eurocodes will be unfamiliar toUK designers; however, the system adopted is common throughout the Eurocodes and theuse of subscripts such as � (temperature), a (steel) and d (design) is relatively straightforward.The Eurocodes operate a hierarchical system whereby definitions found in higher versions ofthe code are generally not repeated. For some of the more common design terms and defini-tions, reference will therefore be required to the main (Part 1.1) versions of the materialcodes. Also in some documents, different terms are given for the same thing; for example,the definition for reduced cross-section (EN 1992-1-2) and effective cross-section(EN 1994-1-2) are identical.



EN 1994-1-2

1.1(16) Inclusion of high-strengthconcrete design

Use information inEN 1992-1-2

—

2.1.3(2) Temperature rise for decayphase

��1 ¼ 200K, ��2 ¼ 200 K —

2.3(1) Design values of mechanicalmaterial properties

1.0 for all cases May be modified in NA forEN 1992-1-2 and EN 1993-1-2

2.3(2) Design values for thermalmaterial properties

1.0 1.0

2.4.2(3) Reduction factor �fi 0.65 or 0.7 for category E Dependent on partial factorsfrom loading codes and basis ofdesign

3.3.2(9) Thermal conductivity Value between upper andlower limit

—

4.1(1) Use of advanced calculationmodels

Any suitable design methodpermitted

Any suitable design methodpermitted

4.3.5.1(10) Buckling length of compositecolumns

0.5 for intermediate column,0.7 for top storey

—

Table 1.2. Definitions from EN 1991-1-2, EN 1992-1-2, EN 1993-1-2 and EN 1994-1-2

Parameter/term Definition Symbol Units

Advanced fire model Design fire based on mass conservation and energyconservation

— —

Axis distance Distance between the axis of the reinforcing bar and thesurface of the concrete

a mm

Box value of sectionfactor

Ratio between the exposed surface area of a notionalbounding box to the section and the volume of steel

ðAm=VÞb m�1

Carbon steel Steel grades referred to in EN 1993, except stainless steels — —

Combustion factor Combustion factor represents the efficiency of combustion,varying between 1 for complete combustion to 0 forcombustion completely inhibited

m —

8





Computational fluiddynamic model

Fire model able to solve numerically the partial differentialequations giving, in all points of the compartment, thethermodynamic and aerodynamic variables

— —

Configuration factor The fraction of diffusely radiated energy leaving surface Athat is incident on surface B

� —

Convective heattransfer coefficient

Convective heat flux to the member related to the differencebetween the bulk temperature of gas bordering the relevantsurface of the member and the temperature of that member

�c W/m2K

Critical temperatureof reinforcement

The temperature of reinforcement at which failure of themember in a fire situation is expected to occur at a givensteel stress level

�s;cr 8C

Critical temperatureof structural steelelement

For a given load level, the temperature at which failure isexpected to occur in a structural steel element for a uniformtemperature distribution

�a;cr 8C

Design fire Specified fire development assumed for design purposes — —

Design fire loaddensity

Fire load density considered for determining thermal actionsin fire design; its value makes allowance for uncertainties

qf;d or qt;d MJ/m2

Design fire scenario Specific fire scenario for which an analysis will be carried out — —

Effective cross-section Cross-section of the member in structural fire design used inthe effective cross-section method. It is obtained byremoving parts with zero strength and stiffness

— —

Effective yield strength For a given temperature, the stress level at which the stress–strain relationship of steel is truncated to provide a yieldplateau

fy;� N/mm2

Emissivity Equal to absorptivity of a surface, i.e. the ratio between theradiative heat absorbed by a given surface, and that of a blackbody surface

" —

Equivalent time of fireexposure

Time of exposure to the standard time–temperature curvedeemed to have the same heating effect as a real fire in a realcompartment

te;d min

External fire curve Nominal time–temperature curve intended for the outside ofseparating external walls which can be exposed to fire fromdifferent parts of the facade, i.e. directly from the inside ofthe respective fire compartment or from a compartmentsituated below or adjacent to the respective external wall

— —

External member Structural member located outside the building that can beexposed to fire through openings in the building enclosure

— —

Fire activation risk Parameter taking into account the probability of ignition,function of the compartment area and the occupancy

— —

Fire compartment Space within a building, extending over one or several floors,which is enclosed by separating elements such that firespread beyond the compartment is prevented for a specifiedfire exposure and for a specified period of time

— —

Fire load Sum of thermal energies which are released by combustionof all combustible materials in a space

Qfi;k MJ

Fire load density Fire load per unit area related to the floor area qf or thesurface area of the total enclosure, including openings, qt

qf , qt MJ/m2

Fire protectionmaterial

Any material or combination of materials applied to astructural member for the purpose of increasing its fireresistance

— —

9





Fire resistance Ability of a structure or a member to fulfil its requiredfunctions (load-bearing function and/or fire-separatingfunction) for a specified load level, for a specified fireexposure and for a specified period of time

R=E=I min

Fire scenario Qualitative description of the course of a fire with time,identifying key events that characterize the fire anddifferentiate it from other possible fires. It typically definesthe ignition and fire growth process, the fully developedstage, decay stage together with the building environmentand systems that will impact on the course of the fire

— —

Fire wall A wall separating two spaces (generally two buildings) that isdesigned for fire resistance and structural stability, and mayinclude resistance to horizontal loading such that, in the caseof fire and failure of the structure on one side of the wall, firespread beyond the wall is avoided

— —

Flash-over Simultaneous ignition of all fire loads in a compartment — —

Fully developed fire State of full involvement of all combustible surfaces in a firewithin a specified space

— —

Global structuralanalysis (for fire)

Analysis of the entire structure, when either the entirestructure, or only a part of it, is exposed to fire. Indirect fireactions are considered throughout the structure

— —

Hydrocarbon firecurve

Nominal time–temperature curve representing the effects ofa hydrocarbon fire

— —

Indirect fire actions Internal forces and moments caused by thermal expansion Various Various

Insulation (I) Ability of a separating element of building construction whenexposed to fire on one side, to restrict the temperature riseof the unexposed face below specified levels

— —

Integrity (E) Ability of a separating element of building construction, whenexposed to fire on one side, to prevent the passage throughit of flames and hot gases and to prevent the occurrence offlames on the unexposed side

— —

Load-bearing function(R)

Ability of a structure or member to sustain specified actionsduring the relevant fire, according to defined criteria

— —

Localized fire Fire involving only a limited area of the fire load in thecompartment

— —

Member Basic part of a structure (such as beam, column, wall, truss)considered as isolated, with appropriate boundary andsupport conditions

— —

Member analysis (forfire)

Thermal and mechanical analysis of a structural memberexposed to fire in which the member is assumed as isolated,with appropriate support and boundary conditions. Indirectfire actions are not considered except those arising fromthermal gradients

— —

Net heat flux Energy, per unit time and surface area, definitely absorbed bymembers

Hnet W/m2

Normal temperaturedesign

Ultimate limit state design for ambient temperaturesaccording to Parts 1.1 of EN 1992 to EN 1996 andEN 1999

— —

One-zone model Fire model where homogeneous temperatures of the gas areassumed in the compartment

— —

10





Opening factor Factor representing the amount of ventilation depending onthe area of openings in the compartment walls, on the heightof these openings and on the total area of the enclosuresurfaces

O m1=2

Part of structure Isolated part of an entire structure with appropriate supportand boundary conditions

— —

Protective layers Any material or combination of materials applied to astructural member for the purpose of increasing its fireresistance

— —

Protected members Members for which measures are taken to reduce thetemperature rise in the member due to fire

— —

Rate of heat release Heat (energy) released by a combustible product as afunction of time

Q W

Reduced cross-section Cross-section of the member in structural fire design used inthe reduced cross-section method. It is obtained from theresidual cross-section by removing parts with assumed zerostrength and stiffness

— —

Section factor For a steel member, the ratio between the exposed surfacearea and the volume of steel; for an enclosed member, theratio between the internal surface area of the exposedencasement and the volume of steel

Am=V m1=2

Separating element Load-bearing or non-load-bearing element forming part ofthe enclosure of a fire compartment

— —

Separating function Ability of a separating element to prevent fire spread orignition beyond the exposed surface during the relevant fire

— —

Simple fire model Design fire based on a limited application field of specificphysical parameters

— —

Stainless steel All steels referred to in EN 1993-1-4 — —

Standard fireresistance

Ability of a structure or part of a structure to fulfil requiredfunctions for the exposure to heating according to thestandard time–temperature curve for a specified loadcombination and for a specified period of time

— —

Standard time–temperature curve

Nominal curve defined in EN 1350126 for representing amodel of a fully developed fire in a compartment

— —

Structural members Load-bearing members of a structure including bracing — —

Temperature analysis Procedure of determining the temperature development inmembers on the basis of the thermal actions (net heat flux)and the thermal material properties of the members and ofprotective surfaces, where relevant

— —

Thermal actions Actions on the structure described by the net heat flux tothe members

— —

Two-zone model Fire model where different zones are defined in acompartment: the upper layer, the lower layer, the fire andits plume, the external gas and walls. In the upper layer,uniform temperature of the gas is assumed

— —

11



CHAPTER 2

Design methods

2.1. IntroductionIn the UK the traditional means of meeting the requirements of the Building Regulations interms of fire resistance of structures has been to rely on tabulated data related to perfor-mance in standard fire tests. The Eurocodes present a range of options for the designerranging from prescriptive rules based on standard fire resistance periods and the use of tabu-lated data, to calculation procedures based on a natural fire exposure and whole buildingbehaviour. The extent to which each of these methods can be used with a particular formof construction is dependent on the state of knowledge regarding the material performancein fire and the availability of suitably validated design methods. The general design proce-dure for the fire limit state indicating the potential routes for compliance with the regulatoryrequirement is summarized in Fig. 2.1.

Table 2.1 summarizes the alternative methods available in the Eurocodes for the verifica-tion of fire resistance for concrete structures. Traditional UK practice generally only consid-ers the most simple element in the matrix.

The hierarchy in terms of complexity is tabulated data followed by simple calculationmethods followed by advanced calculation methods. For the designer the tabulatedapproach should be the first port of call and should be suitable for the vast majority ofstructures. Calculation methods can be used to demonstrate performance under specificconditions and may provide substantial savings in certain circumstances. Advanced calcula-tion methods (typically non-linear finite-element models) may be used where the structure isvery complex and where the provisions of the National regulations are not applicable.Examples of such structures would include sports stadia, exhibition halls or airportterminals.

The Eurocode approach to structural design will be unfamiliar to many UK engineers.However, there are a number of similarities between the approaches adopted. The standarddesign route will remain the use of tabulated data with reference to specified periods of fireresistance related to the standard fire test. The most significant difference in approach is onewhich is not restricted to the use of the fire parts of the material codes but is perhaps morepronounced in this area. The information required to carry out structural fire engineeringdesign has traditionally been located within one material code. The structural Eurocodesare an integrated suite of design standards and are meant to be used as such. To carry outa design for concrete structures, for example, using tabulated values from the Nationalstandards, the designer needs only refer to the relevant National material codes. For asimilar design to the Eurocode it is necessary to obtain partial factors from EN 1990,information on loads from EN 1991-1, information on the thermal and mechanical responsefrom EN 1991-1-2 and finally obtain the required dimensions from EN 1992-1-2. Althoughthe fire design methodology adopted in the Eurocodes is radically different from theprocedures generally used in the UK, the end result, in terms of member sizes and coverto reinforcement is, in many cases, similar.


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Designprocedure

14



In the fire parts of the various material codes (EN 1992-1-2, EN 1993-1-2, EN 1994-1-2),fire resistance may be determined either by:

. simple calculation models

. advanced calculation models, or

. tabulated data.

The current UK Standards are based on tabulated periods of fire resistance derived fromstandard fire tests and fire resistance derived from calculations in certain specific cases.

The regulatory requirement is generally specified in National regulations based on thetype of occupancy (office, domestic, retail, etc.) and the height of the structure. The designprocedure from the Eurocodes indicating the relationship between the various standardsrequired for design is as follows:

. selection of relevant design fire scenario (EN 1991-1-2)

. determination of corresponding design fire (EN 1991-1-2)

. calculation of the temperature rise of the structural members (EN 1992-1-2, EN 1993-1-2,EN 1994-1-2)

. calculation of the mechanical response (EN 1992-1-2, EN 1993-1-2, EN 1994-1-2).

The situation is illustrated schematically in Fig. 2.2.The most significant difference in approach is that load effects both in relation to dead

and imposed loading and the time–temperature regime to be used for assessment are notcontained within the material code but in the relevant codes for actions on structures.

In the Eurocodes, simple calculation methods are based on an assessment of the deteriora-tion in material properties at elevated temperature together with an assessment of theappropriate load for the fire limit state. The resistance is then calculated based on reductionfactors appropriate to the design thermal exposure and compared to the load effects presentat the time of the fire. Advanced calculation methods typically involve the use of complexfinite-element models and would not in general be available to designers.

Table 2.1. Alternative methods for verification of fire resistance to EN 1992-1-2

Tabulated data:prescriptive methods

Simplified calculationmethods

Advancedcalculationmethods

Member analysis. Themember is considered asisolated. Indirect fireactions are notconsidered, except thoseresulting from thermalgradients

YES. Data given for

standard fire only. In principle, data

could be developedfor other firecurves

YES. Standard fire andparametric fire

. Temperature profiles givenfor standard fire only

. Material models apply onlyto heating rates similar tostandard fire

YES. Only theprinciplesare given

Analysis of parts of thestructure. Indirect fireactions within the sub-assembly are considered,but no time-dependentinteraction with otherparts of the structure

NO YES. Standard fire andparametric fire

. Temperature profiles givenfor standard fire only

. Material models apply onlyto heating rates similar tostandard fire


Global structuralanalysis. Analysis of theentire structure. Indirectfire actions are consideredthroughout the structure

NO NO YES. Only theprinciplesare given

15

CHAPTER 2. DESIGN METHODS


2.2. Design of concrete structures to EN 1992-1-2The Eurocode design procedure for concrete structures subject to fire is classified accordingto the design method adopted which may be tabulated data, simple calculation models oradvanced calculation models. The options available to the designer are summarized inTable 2.2.

Table 2.2. Range of options available to the designer

Thermal model Structural model Method of analysis

Nominal (standard) fire curves Single element Tabulated data

Calculation based on standard curve(time equivalent)

Sub-assembly Simple calculation models

Simple calculation based oncompartment characteristics(parametric approach)

Entire structure Advanced calculation models(non-linear finite elements)

Advanced calculation model(computational fluid dynamics)

— —

Tabulated data are presented for reinforced concrete columns, walls (both load-bearingand non-load-bearing), beams (including simply supported and continuous, and reinforcedand prestressed), and slabs (both solid and ribbed). Simplified calculation methods arepresented together with appropriate strength reduction values. Two simple calculationmethods, namely the 5008C isotherm method and the zone method, are given in Annex Bof the code. General guidance is given on advanced methods for the determination of thetemperature profile and the mechanical response of concrete structures.

2.3. Design of steel structures to EN 1993-1-2The Eurocode design procedure for steel structures subject to fire is classified according tothe type of analysis undertaken. The analysis may be undertaken for a single member, apart of the structure or a global analysis of the entire structure. The options available tothe designer are summarized in Table 2.3. Simple calculation methods are presented fortension members, compression members, and members in bending. Verification may becarried out in relation to either resistance or temperature.

Step 1Determine fire resistance requirements(National regulations (AD-B), Fire engineering

Step 2Calculate load effects at the fire limit state(EN 1990/EN 1991-1/EN 1991-1-2/EN 1992-1,EN 1993-1, EN 1994-1)

Step 3Choose the relevant dimensions to meet the requirements obtained in Step 1 (EN 1992-1-2, EN 1993-1-2, EN 1994-1-2)

Fig. 2.2. Simplified fire design procedure

16



2.4. Design of composite structures to EN 1994-1-2The Eurocode design procedure for composite steel and concrete structures subject to fire isclassified both according to the type of analysis undertaken and the design procedureadopted. The options available to the designer are summarized in Table 2.4. Tabulated


Tabulated data:prescriptivemethods Simplified calculation methods


Member analysis. Themember is considered asisolated. Indirect fire actionsare not considered, exceptthose resulting from thermalgradients

NO YES. Standard fire and parametric

fire. Temperature profiles for

protected or unprotectedsteel members can becalculated

YES. Refer toNationalAnnex

Analysis of parts of thestructure. Indirect fire actionswithin the sub-assembly areconsidered, but no time-dependent interaction withother parts of the structure

NO NO YES. Refer toNationalAnnex

Global structural analysis.Analysis of the entirestructure. Indirect fire actionsare considered throughout thestructure

NO NO YES. Refer toNationalAnnex


Tabulated data:prescriptivemethods Simplified calculation methods


Member analysis. Themember is considered asisolated. Indirect fire actionsare not considered, exceptthose resulting from thermalgradients

YES – datagiven forstandard fireonly

YES – only valid forstandard fire exposure. Standard fire and parametric

fire. Temperature profiles for

protected or unprotectedsteel members can becalculated


Analysis of parts of thestructure. Indirect fire actionswithin the sub-assembly areconsidered, but no time-dependent interaction withother parts of the structure


Global structural analysis.Analysis of the entirestructure. Indirect fire actionsare considered throughout thestructure


17

CHAPTER 2. DESIGN METHODS


data are presented for composite beams with partial encasement and composite columns(including totally encased steel sections, partially encased steel sections and concrete-filled hollow sections). Simple calculation models are presented for composite slabs andcomposite beams (including bare steel beams and partially encased steel beams) and for com-posite columns. General guidance is given on the use of advanced calculation models forthe calculation of thermal and mechanical response.

2.5. Design assisted by testingFor all materials considered in this handbook fire design may be based on the results of firetests as an alternative to design by calculation. Design may be based on a combination oftests and calculations.

18



CHAPTER 3

Design fires

3.1. IntroductionThe first stage in a structural fire engineering design is to define the appropriate fire designscenario. This will typically involve a consideration of a fire in various compartmentswithin a building to establish the most suitable cases for design purposes. The choice ofthe design fire scenario will dictate the choice of design fire to be used. A determination ofthe thermal actions to be used in subsequent structural analysis can be achieved eitherthrough a prescriptive approach, which relies on data from standard test methods, orfrom a consideration of the physical parameters specific to a particular building. Theformer approach is consistent with the current prescriptive methods used by most designersin the UK. The latter method allows for calculation procedures and represents a radicaldeparture from traditional fire design. There are effectively four levels or models, whichcan be used to determine the thermal exposure. These are described in Table 3.1 in orderof increasing complexity, based on a matrix representation by Witteveen.27

To date, level 3 and 4 solutions have been restricted to research projects or complex andinnovative structures. The implementation of the Eurocodes will allow a larger number ofbuildings to be designed according to the calculation procedures in the codes. Regulatorybodies have increasingly been moving away from a prescriptive approach towards a func-tional methodology whereby the designer is told what must be achieved but not how tomeet the functional requirements. This freedom of choice allows the designer a range ofoptions including the use of calculation procedures.

Table 3.1. Assessment methods for thermal exposure

Assessmentmethod

Model for thermalexposure Description

Level 1 H1 Standard fire exposure – test or tabulated data

Level 2 H2 Equivalent fire duration time – relates the severity of acompartment fire to an equivalent period in a standard furnace

Level 3 H3 Parametric exposure – uses physical characteristics of the firecompartment as input parameters

Level 4 H4 Advanced methods – zone or field models used to characterizethe full compartment response for the required duration

3.2. General rules for calculating atmosphere temperaturesThe thermal actions to be used in subsequent analysis may be either nominal, derived fromsimple calculation, or by advanced methods. The choice of a particular fire design scenario


should be based on a risk assessment taking into account the likely ignition sources and anyfire detection/suppression methods available. The design fire should be applied to only onefire compartment at a time.

3.3. Nominal temperature–time curvesThe nominal or standard fire curves provide a simple means of assessing building materialsand components against a common set of performance criteria subject to a closely definedthermal and mechanical loading under prescribed loading and support conditions. Althoughnotionally a representation of building fires, the standard fire curves do not take into accountany of the physical parameters affecting fire growth and development. The nominal curvesgiven in EN 1991-1-2 are described below.

3.3.1. Standard temperature–time curveThe standard fire curve has been used effectively for many years to determine the relativeperformance of construction materials. The temperature–time relationship is describedbelow and set out in EN 1363.20

�g ¼ 20þ 345 log10ð8tþ 1Þ ð3:1Þ

where:

�g is the gas temperature in the fire compartment (8C); andt is the time (min).

One crucial shortcoming of this (and the other nominal curves) is that there is nodescending branch, i.e. no cooling phase. Large-scale experiments28 have shown that thecooling phase can be very important with regard to structural performance, particularlywhere large thermal restraint is present. This standard relationship is the basis for thetabulated data in the codes for steel, concrete and composite construction. Many ofthe design methods available through the Eurocodes are restricted to the choice of adesign fire similar to the standard curve, as there is insufficient information on the thermaland structural performance of members and complete structures subject to natural fireexposures.

3.3.2. External fire curveThe external fire curve is used for structural members in a facade external to the mainstructure. The external fire curve is given by:

�g ¼ 660ð1� 0:687 e�0:32t � 0:313 e�3:8tÞ þ 20 ð3:2Þ

where �g and t are as defined above.

3.3.3. Hydrocarbon curveIn situations where petrochemicals or plastics form a significant part of the overall fire load,the temperature rise is very rapid due to the much higher calorific values of these materials.Therefore, for such situations, an alternative temperature–time curve has been developed ofthe form:

�g ¼ 1080ð1� 0:325 e�0:167t � 0:675 e�2:5tÞ þ 20 ð3:3Þ

The three nominal curves defined in the Eurocodes are illustrated in Fig. 3.1 together with atypical natural fire exposure consisting of an ignition phase, a growth phase, a steady-statephase and a decay phase. A number of other nominal fire curves are used for specificcircumstances such as assessing linings for tunnels. These curves are not included in theEuropean standards. More information is available in the literature.29

20



3.4. Equivalent time of fire exposureEN 1991-1-2 includes a method for determining the appropriate fire resistance period fordesign based on a consideration of the physical characteristics of the fire compartment.This is effectively a ‘halfway house’ between the nominal curves so familiar to many andthe behaviour of a realistic fire compartment. The method relates the severity of a real firein a real compartment to an equivalent period of exposure in a standard test furnace. Therelevant input parameters are the amount of fire load, the compartment size (floor areaand height), the thermal properties of the compartment linings and the ventilationconditions. The formulation in the Eurocode (based on fire load density related to floorarea) is:

te;d ¼ ðqf;dkbwtÞkc ð3:4Þ

where:

te;d is the equivalent time of fire exposure for design (min);qf;d is the design fire load density (MJ/m2);kb is a conversion factor dependent on thermal properties of linings;wt is the ventilation factor; andkc is a correction factor dependent on material. (Note: for protected steel and reinforced

concrete kc ¼ 1:0, where no detailed assessment of the thermal properties is made thefactor kb ¼ 0:09 (National Annex value).)

The ventilation factor is:

wf ¼ ð6=HÞ0:3½0:62þ 90ð0:4� �vÞ4�in the absence of horizontal openings (roof lights) in the compartment;

where:

H is the height of the fire compartment (m); and�v ¼ Av=Af where Av and Af are the ventilation and floor area respectively (m2).

The verification is then that the fire resistance of the member is greater than the timeequivalent value. The concept of time equivalence is illustrated in Fig. 3.2 with respect tothe maximum temperature of a structural member and the time taken for that member toachieve an identical temperature in a standard furnace test.

The concept is illustrated with reference to a worked example.

1200

1000

800

600

400

200

00 20 40 60 80 100 120 140

Time (min)

Tem

pera

ture

(°C

)

ISO External Hydrocarbon Natural fire

Fig. 3.1. Nominal fire curves – comparison with results from natural fire test

21

CHAPTER 3. DESIGN FIRES


1200

1000

800

600

400

200

0

Tem

pera

ture

(°C

)

0 15 30 45 60 75 90

Time (min)

Max. steel temp.

Te

Atmosphere(fire)

Atmosphere(furnace)

Steel(fire)

Steel(furnace)

Fig. 3.2. Concept of time equivalence (with reference to structural steel member). Courtesy Dr B. Kirby

Example 3.1: Time equivalent calculationCalculate the appropriate fire resistance period for a protected steel beam within a smalloffice with boundaries of fire-resistant construction (compartment floors and walls).Let us consider a small fire compartment within an office building – design parameters.

Tables 3.2 to 3.5 below refer.

Table 3.2. Geometric data

Description Data

Floor area Af (m2) 36 (6m� 6m)

Ventilation area Av (m2) 7.2 (3.6m wide� 2m high)

Height of ventilation opening h (m) 2Height of compartment H (m) 4

Table 3.3. Material thermal data

Element Material Thermal inertia (b value – J/m2 s1=2K) Area (m2)

Roof Concrete 2280 36Floor Plasterboard 520 36Walls Plasterboard 520 76.8

Table 3.4. Factor kb to account for thermal properties of compartment linings

Thermal properties Data

b ¼ ð�c�Þ1=2 ( J/m2 s1=2K) kb (minm2/MJ)b > 2500 0.04 (0.055)720 � b � 2500 0.055 (0.07)b < 720 0.07 (0.09)

Note: UK National Annex values in brackets.

22



3.5. Parametric temperature–time curvesAlong with the time equivalent approach, parametric fires are an example of the simplecalculation methods for determining the compartment internal atmosphere time–temperature relationship. The current approach has been modified (in scope) in successivedrafts of the fire part of Eurocode 1. The basic formulation has remained largely unchangedhowever and is based on work carried out by Wickstrom.30 The parametric approachprovides a quick and easy approximation of compartment gas temperatures ideally suitedfor use on modern spreadsheets. The approach has been extensively validated over anumber of years. It applies only to the post-flashover phase, which is of primary concernwhen considering structural issues and assumes a uniform temperature within the compart-ment. The basic formulation in Annex A of EN 1991-1-2 is as follows:

�g ¼ 20þ 1325ð1� 0:324 e�0:2t� � 0:204 e�1:7t� � 0:472 e�19t� Þ ð3:5Þ

where:

�g is the temperature in the fire compartment (8C);t� ¼ t� (h);t is time (h);� ¼ ½O=b�2=ð0:04=1160Þ2;b ¼ pð�c�Þ (J/m2 s1=2K);O ¼ opening factor ðAv

ph=AtÞ (m1=2);

Av is the area of vertical openings (m2);h is the height of vertical openings (m);At is the total area of enclosure (m2);� is the density of boundary enclosure (kg/m3);c is the specific heat of boundary of enclosure (J/kgK); and� is the thermal conductivity of boundary (W/mK).

The temperature within any given compartment is assumed to vary as a simple exponentialfunction of modified (or parametric) time, depending on the variation in the ventilation area

Table 3.5. Characteristic fire load density

Occupancy Characteristic fire load density qf;k (MJ/m2) – 80% fractile

Dwelling 948 (870)Hospital 280 (350)Hotel 377 (400)Office 511 (570)School classroom 347 (360)

Note: UK values from PD 7974-125 in brackets.

For the worked example using relevant values for the UK:

Design fire load density qf;d ¼ qf;k ¼ 570MJ/m2

Ventilation factor wf ¼ 0:863 (�v ¼ 0:2)Factor to account for thermal properties kb ¼ 0:07 (b ¼ 945 J/m2 s1=2 K)Construction material factor kc ¼ 1:0 (protected steel beam)Then from equation (3.4):

te;d ¼ 570� 0:863� 0:07 ¼ 34min

Therefore 60min fire protection would be appropriate.

23



and the properties of the compartment linings. The values 0.04 and 1160 refer to the openingfactor and thermal properties of the compartment used in the development of the approach.A parametric calculation with the same values corresponds to a time–temperature responsevery similar to the standard fire curve.

In the original draft for development of the Eurocode released for use in the UK with theUK National Application Document31 there were a number of restrictions on the use of thisformula, which greatly limited the scope of application. Most of these have now beenremoved as validation for the approach has been developed and the method may now beused for most common building types.

The calculation procedure provides the engineer with a rate of temperature rise varyingwith time. In order to estimate the duration of the fire, the relationship between the fireload and the opening must be considered. The maximum temperature in the heating phaseoccurs at a time tmax given by:

tmax ¼ maximum of 0:2� 10�3 � qt;d=O or tlim ð3:6Þ

where qt;d is the design value of the fire load density related to the total surface area of theenclosure (values of qt;d should be in the range 50–1000MJ/m2); and tlim is a minimumvalue for the duration of the fire based on slow, medium or fast fire growth rates. Foroffice accommodation a medium fire growth rate should be assumed corresponding to avalue of tlim equal to 20min.

For most practical combinations of fire load, compartment geometry and opening factortmax will be in excess of the 20-minute limit. The temperature–time curves for the coolingphase are then given by:

�g ¼ �max � 625ðt� � t�maxÞ for t�max � 0:5 ð3:7aÞ

�g ¼ �max � 250ð3� t�maxÞðt� � t�maxÞ for t�max < 2 ð3:7bÞ

�g ¼ �max � 250ðt� � t�maxÞ for t�max � 2 ð3:7cÞ

Example 3.2 shows an example of a parametric calculation for a typical office compart-ment while Fig. 3.3 shows the predicted time–temperature response together with testresults indicating the accuracy of the approach. The reader will note the similarities withthe calculation procedure for time equivalence discussed above.

Average compartment time–temperature response

0 10 20 30 40 50 60 70Time (min)

Average test 1 Average test 2 BS 476 EC1

1200

1000

800

600

400

200

0

Tem

pera

ture

(°C

)

Fig. 3.3. Comparison between parametric prediction and test results

24



Example 3.2: Parametric calculationA typical fire compartment within an office building has a floor area of 6m� 6m and afloor-to-ceiling height of 3.4m. There is a single window opening in the front elevation3.6m wide� 2m high. Table 3.6 summarizes the geometric parameters required for thecalculation of the compartment time–temperature response.

Table 3.6. Geometric parameters for parametric calculation

Description Data

Floor area Af (m2) 36 (6m� 6m)

Ventilation area Av (m2) 7.2 (3.6m wide� 2m high)

Total area of compartment boundaries(including windows) (m2)

153.6 ½ð2� 6� 6Þ þ ð4� 3:4� 6Þ�

Height of ventilaion opening h (m) 2Opening factor Oðm1=2Þ ¼ ðAv

phÞ=At 0.066

The walls and floor are lined with gypsum-based plasterboard and the ceiling is con-structed from precast concrete planks. Table 3.7 summarizes the material propertiesrequired for the calculation of the compartment time–temperature response.

The b value to be used for design is a weighted average where b ¼ �ðbjAj=AjÞ. Here therelevant b value to be used in the design is 945 J/m2 s1=2K.

Table 3.7. Thermal properties for parametric calculation

Construction MaterialThermal inertia(b value – J/m2 s1=2K) Area (m2)

Roof Concrete 2280 36Floor Plasterboard 520 36Walls Plasterboard 520 76.8

No information on the thermal properties of commonly used construction materials isprovided in the Eurocode. Some guidance is available in the literature and this isreproduced in Table 3.8. The main values for thermal inertia are taken from CompetitiveSteel Buildings Through Natural Fire Safety Concept,32 with the values in brackets takenfrom the CIB W14 Workshop Report, Design guide: structural fire safety.33 Thediscrepancies in b value are indicative of the variation in supposedly similar materials.Clearly more information is required in this area. Wherever possible, designers shouldconsult manufacturers to obtain accurate material property data for calculations.

Table 3.8. Thermal properties of commonly used construction materials

Material Thermal inertia b value ( J/m2 s1=2K)

Normal-weight concrete 2034.7 (2280)Lightweight concrete 1122.5 (840)Structural steel 13 422.3 (15 000)Calcium silicate board 151.8Timber 223.8 (600)Brick 1521.5 (1200)

The characteristic fire load density is generally taken as the 80% fractile figurereproduced in the Eurocode. In this case a design fire load density of 570MJ/m2 has

25



3.6. External atmosphere temperatureExternal structural members may be exposed to fire by flames and radiated heat emanatingfrom openings in the building. Annex B of EN 1991-1-2 provides a calculation approach fordetermining thermal actions for external members based on work carried out by Law.34

The method allows for the calculation of the maximum compartment temperature, the sizeand temperature of the flame plume emerging from the openings, and the heat transfer para-meters for radiation and convection.

3.7. Advanced fire modelsIn certain circumstances it may be necessary to go beyond a reliance on nominal fireexposures or simple calculation methods. Advanced methods, including zone modelsbased on a solution of the equations for conservation of mass and energy or morecomplex computational fluid dynamics (CFD) models, may be used to provide informationbased on a solution of the thermodynamic and aerodynamic variables at various pointswithin the control zone. Such models have been used effectively for many years to modelthe movement of smoke and toxic gases and are now being extended to model the thermalenvironment for particular post-flashover fire scenarios. Such complex models are notgenerally available to structural engineers responsible for the fire engineering design ofbuildings and would generally be used by research institutions or specialist fire engineeringconsultants.

been used. Fire load densities are published in both EN 1991-1-2 and UK Standards25 andthe CIB Design Guide.33 The relevant information is given in Table 3.9 with the mainfigures coming from the Eurocode and the figures in brackets from the UK Standard.The source data for fire load density may be found in the CIB Design Guide and, itshould be noted, display a wide variation depending on the country of origin and theprecise nature of the occupancy. The codified values are not always in agreement withone another and, in certain cases, such as the characteristic values quoted in the Europeanand UK codes for residential accommodation, give very different answers. Again morework is required to rationalize these critical design parameters.

Table 3.9. Fire load densities

Occupancy Characteristic fire load density (MJ/m2) – 80% fractile

Dwelling 948 (400)Hospital 280 (350)Hotel 377 (400)Office 511 (570)School classroom 347 (360)

With these input values, equations (3.5) and (3.6) are used to calculate the compartmenttime–temperature response and the anticipated duration. In this case the parametricequation predicts a maximum temperature of 9958C and a time to maximum temperatureof 24min. The predicted response is illustrated in Fig. 3.3 and compared to measuredvalues from two real fire tests.

26



CHAPTER 4

Member temperatures

4.1. IntroductionThe calculation of the atmosphere temperatures within the fire compartment presented in theprevious chapter is the first step in a rational fire engineering design process. The next step isto determine, either through calculation or reference to published data, the temperaturedistribution within the structural elements.

4.2. Section factors for steel and composite constructionThe section factor A=V is a convenient parameter to measure the thermal response of a steelmember. Basically, the rate at which a steel beam or column will increase in temperature isproportional to the surface area (A) of steel exposed to the fire and inversely proportional tothe mass or volume (V) of the section. In a fire, a member with low section factor will heat upat a slower rate than one with high section factor.

Calculation of the section factor for different types of unprotected section is shown inFig. 4.1.

4.3. Unprotected steelworkEN 1993-1-2 provides a simple design approach for calculating the thermal response ofunprotected steel members. This approach can be extended to other metals includingwrought iron, cast iron, aluminium alloys and stainless steels.

Assuming an equivalent uniform temperature distribution in a cross-section, theincrease of temperature ��a;t [K] in an unprotected steel member during a time interval�t is given by:

��a;t ¼ kshAm=V

ca�a_hhnet;d �t for �t � 5 s ð4:1Þ

where:

�a is the unit mass of steel (kg/m3);Am is the surface area of the member per unit length (m2);Am=V is the section factor for unprotected steel members (m�1);ca is the specific heat of steel (J/kgK);_hhnet;d is the net heat flux per unit area (W/m2);ksh is the correction factor for the shadow effect (ksh ¼ 1:0 if the shallow effect is

ignored);�t the time interval (s); andV is the volume of the member per unit length (m3).


For cross-sections with a convex shape, such as rectangular or circular hollow sections,fully embedded in fire, the shadow effect does not play a role and it can be taken asksh ¼ 1:0. Otherwise, the correction factor for the shadow effect ksh is given by:

ksh ¼

0:9½Am=V �bAm=V

for I-sections under nominal fire actions

½Am=V �bAm=V

for other cases

8>>><>>>:

where Am=V � 10m�1; and [Am=V �b is the box value of the section factor.

4.4. Steelwork insulated by fire protectionEN 1993-1-2 provides a simple design approach for insulated steel members with non-reactive fire protection materials. The insulating materials can be in the form of profiledor boxed systems, but do not include intumescent coatings. Assuming uniform temperaturedistribution, the temperature increase ��a;t of an insulated steel member during a timeinterval �t (� 30 s) is given by:

��a;t ¼�pAp=V

dpca�a

ð�g;t � �a;tð1þ �=3Þ �tðe�=10 � 1Þ��g;t but ��a;t � 0 if ��g;t > 0 ð4:2Þ

with

� ¼cp�pca�a

dpAp=V

Sketch Description Section factor Am/V

Open section exposed to fireon all sides

Open section exposed to fireon three sides

I-section flange exposed to fireon three sides

Angle exposed to fire onall sides

Tube exposed to all sides

Hollow section or welded box section exposed to all sides

b

h

t

btf

Am perimeter = V cross-sectional area

Am 1 ≈ for t << b V t

Am 2 = V t

Am 1 = V t

Am 1 ≈ for tf << b V tf

Am b + 2tf = or V btf

Am surface exposed to fire = V cross-sectional area

Am 2(b + h) = or V cross-sectional area

Fig. 4.1. Section factor for unprotected steel members

28



where:

�p is the thermal conductivity of fire protection material (W/mK);�a;t is the steel temperature at time t (8C);�g;t is the ambient gas temperature at time t (8C);��g;t is the increase of ambient gas temperature during time interval �t (K);�a is the unit mass of steel (kg/m3);�p is the unit mass of fire protection material (kg/m3);Ap=V is the section factor for steel members insulated by fire protection material (m�1);Ap is the appropriate area of fire protection material per unit length (m2);ca is the temperature-dependent specific heat of steel (J/kgK);cp is the temperature-independent specific heat of fire protection material (J/kgK);dp is the thickness of fire protection material (m);�t is the time interval (s); andV is the volume of the steel member per unit length (m3).

Figure 4.2 illustrates some design values of the section factors Ap=V for insulated steelmembers. It is worth noting that the area Ap of the fire protection material is generallytaken as the area of its inner surface. For hollow encasement with a clearance around thesteel members, the value of Ap is taken as that for hollow encasement without a clearance.

Sketch Description Section factor Ap/V

Contour encasement of uniform thickness

Contour encasement ofuniform thickness, exposed to fire on 3 sides

Hollow encasement of uniform thickness.(The clearance c1 and c2 < h/4)

Hollow encasement of uniform thickness, exposed to fire on 3 sides (The clearance c1 and c2 < h/4)

h h

bb

h h

b

Ap 2h + b = V steel cross-sectional area

Ap 2(b + h) = V steel cross-sectional area

Ap steel perimeter – b = V steel cross-sectional area

Ap steel perimeter = V steel cross-sectional area

c1 c2

bb c1 c2

Fig. 4.2. Section factor for insulated steel members

Temperature (°C)

Timet1 t1 + td

Moisture plateau – timedelay td

100

Fig. 4.3. Evaluation of moisture plateau for protection materials (DD ENV 13381-4: 2002)

29

CHAPTER 4. MEMBER TEMPERATURES


For moist fire protection materials, the steel temperature increase��a may be modified toallow for a time delay td in the rise of the steel temperature when it reaches 1008C, due to thelatent heat of vaporization of the moisture, as shown in Fig. 4.3. The calculation method fortd is given in DD ENV 13381-4 (2002).35

4.5. Unprotected composite slabsEN 1994-1-2 provides the simple calculation models for determining the sagging and hoggingmoment resistances of unprotected composite slabs with profiled steel decking exposed to thestandard fire. The evaluation of the temperature profiles within the slab is given in its AnnexD (informative).

The approach allows the temperatures of the steel sheet, reinforcement bars in the ribs andthe concrete slab to be calculated separately. The temperatures of the lower flange, web andupper flange of the steel decking, and the reinforcement bars in the ribs can be obtained byusing the empirical formulae. However, the calculation of temperature profiles for the con-crete part of the slabs is rather complicated as the temperature distribution across a concretecross-section exposed to fire conditions will not be uniform. It will be too complicated toestablish the isotherms within the concrete by using empirical formulae.

Currently, EN 1994-1-2 only provides a simple model for establishing the isotherm for acertain limiting temperature within the concrete, with temperatures beyond the limitingtemperature being neglected and the remaining cross-section being taken as ambient tem-perature. It must be emphasized that the limiting temperature is derived from equilibriumover the cross-section and has no relation with temperature penetration.36 Such simplifica-tion may be adequate for the calculation of hogging moment resistance, but not for thethermal response analysis of the slabs. Alternatively, EN 1994-1-2 provides a conservativeapproximation by treating the composite slabs as solid slabs with the temperature distribu-tion given in a table.

One assumption of the method is that the steel deck remains bonded to the concrete.Evidence from fire tests suggests that this is not a valid assumption.

4.5.1. Steel deckingThe temperatures �a of the lower flange, web and upper flange of the steel decking are givenby:

�a ¼ b0 þ b11

l3þ b2

A

Lr

þ b3�þ b4�2 ð4:3Þ

with

� ¼ 1

l3

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih22 þ

�l3 þ

l1 � l22

�2s�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih22 þ

�l1 � l2

2

�2s24

35

where:

� is the view factor of the upper flange;b0 . . . b4 are the coefficients for determining the temperatures of various parts of the

steel decking as given in Table 4.1;A=Lr is the rib geometry factor (mm);A is the concrete volume of the rib per metre rib length (mm3/m);h2 is the depth of the rib (mm);Lr is the exposed area of the rib per metre rib length (mm2/m);l1; l2 are the distances as shown in Fig. 4.4 (mm); andl3 is the width of the upper flange (mm).

The definition of the geometric dimensions and factors of a typical composite slab is givenin Fig. 4.4.

30



4.5.2. Reinforcement barsThe temperature �s of the reinforcement bars in the rib (see Fig. 4.5) is given by:

�s ¼ c0 þ c1u3h2

þ c2zþ c3A

Lr

þ c4�þ c51

l3ð4:4Þ

with

1

z¼ 1ffiffiffiffiffi

u1p þ 1ffiffiffiffiffi


u3p

where:

� is the angle of the web (degrees);c0 . . . c5 are the coefficients for determining the temperature of rebars in the rib as given

in Table 4.2;A=Lr is the rib geometry factor (mm);A is the concrete volume of the rib per metre rib length (mm3/m);

Table 4.1. Coefficients for determining temperatures of various parts of steel decking

Concrete

Standardfireresistance

Part ofsteelsheet

b0(8C)

b1(8Cmm)

b2(8Cmm)

b3(8C)

b4(8C)

Normal- R60 Lower flange 951 �1197 �2.32 86.4 �150.7weight Web 661 �833 �2.96 537.7 �351.9concrete Upper flange 340 �3269 �2.62 1148.4 �679.8

R90 Lower flange 1018 �839 �1.55 65.1 �108.1Web 816 �959 �2.21 464.9 �340.2Upper flange 618 �2786 �1.79 767.9 �472.0


Lightweight R30 Lower flange 800 �1326 �2.65 114.5 �181.2concrete Web 483 �286 �2.26 439.6 �244.0

Upper flange 331 �2284 �1.54 488.8 �131.7R60 Lower flange 955 �622 �1.32 47.7 �81.1

Web 761 �558 �1.67 426.5 �303.0Upper flange 607 �2261 �1.02 664.5 �410.0



Note: For intermediate values, linear interpolation is allowed.

h1

l1l3/2

l2

h2 I1 – I2

2

I2 + 2 h22 + ( )

2

Area: A

Lr

Concrete slab

Steel sheet

The rib geometry factor A/Lr is given by:

I1 + I2h2 ( ) 2A

=Lr

Fig. 4.4. Definition of geometric dimensions of composite slabs

31



h2 is the depth of the rib (mm);Lr is the exposed area of the rib per metre rib length (mm2/m);l3 is the width of the upper flange (mm);u1; u2 are the shortest distance from the rebar centre to any point of the webs (mm);u3 is the distance from the rebar centre to lower flange (mm); andz is the factor indicating the position of rebar in the rib (mm�1=2).

Figure 4.5 illustrates how to measure the distances u1, u2 and u3 for the reinforcement barsin the ribs of a composite slab.

4.5.3. Concrete slab over steel deckingFor the concrete slab over trapezoidal or dovetail steel decking, EN 1994-1-2 doesnot provide a simple model for calculating the temperature distribution. It does, however,provide a temperature distribution based on an equivalent solid slab.

In the calculation, the composite slab is replaced by a solid slab with an effective thicknessheff which is given by:

heff ¼h1 þ 0:5h2

�l1 þ l2l1 þ l3

�for h2=h1 � 1:5 and h1 > 40mm

h1

�1þ 0:75

�l1 þ l2l1 þ l3

��for h2=h1 > 1:5 and h1 > 40mm

8>>><>>>: ð4:5Þ

Rebar

αu2

u3

u1Rebar

u2

u3

u1

Fig. 4.5. Definition of u1, u2 and u3 for rebar in the rib

Table 4.2. Coefficients for determining temperatures of rebars in the rib

ConcreteStandard fireresistance

c0(8C)

c1(8C)

c2(8Cmm0:5)

c3(8Cmm)

c4(8C/8)

c5(8Cmm)

Normal- R60 1191 �250 �240 �5.01 1.04 �925weight R90 1342 �256 �235 �5.30 1.39 �1267concrete R120 1387 �238 �227 �4.79 1.68 �1326

Lightweight R30 809 �135 �243 �0.70 0.48 �315concrete R60 1336 �242 �292 �6.11 1.63 �900

R90 1381 �240 �269 �5.46 2.24 �918R120 1397 �230 �253 �4.44 2.47 �906

Note: For intermediate values, linear interpolation is allowed.

Screed

Concrete

Steel sheetl2

l1 l3

l3 l1

l2

h2

h1

h3

Fig. 4.6. Cross-sectional dimensions of composite slabs

32



where the cross-section dimensions h1, h2, l1, l2 and l3 are given in Fig. 4.6. The temperatureat a depth x from heff can then be obtained from Table 4.3.

4.6. Temperature profile for concrete membersAnnex A (informative) of EN 1992-1-223 provides a series of calculated temperature profilesfor slabs or walls, beams and columns. The available design charts are summarized in Table4.4.

Table 4.4. Summary of design charts for concrete members

Member Cross-sectional dimensions (mm) Standard fire resistance

Slabs or walls exposed to one side Thickness¼ 200 R30–R240

Beams Height�width¼ 300� 160 R30–R90 and 5008C isothermsHeight�width¼ 600� 300 R60–R120Height�width¼ 800� 500 R60–R240

Square columns Height�width¼ 300� 300 R30–R120 and 5008C isotherms

Circular columns Diameter¼ 300 R30–R120 and 5008C isotherms

The design charts are based on the following assumptions:

. The specific heat of concrete corresponds to 1.5% of moisture content.

. The lower limit of thermal conductivity is used.

. The emissivity of concrete surface is 0.7.

. The convection factor is 25.

. The spalling of concrete does not occur during fire exposure.

Figure 4.7 shows the temperature profiles for slabs with thickness¼ 200mm and 600mmfor R30 to R240. Figure 4.8 shows the temperature profiles for beams with width� height¼ (160� 230mm) and (300� 600mm) for R30 to R120.

Table 4.3. Temperature distribution in a 100mm thick solid slabof normal-weight concrete and not insulated

DepthTemperature �c (8C) for standard fire resistance of

x (mm) R30 R60 R90 R120 R180 R240

5 535 705 — — — —10 470 642 738 — — —15 415 581 681 754 — —20 350 525 627 697 — —25 300 469 571 642 738 —30 250 421 519 591 689 74035 210 374 473 542 635 70040 180 327 428 493 590 67045 160 289 387 454 469 64550 140 250 345 415 430 55055 125 200 294 369 549 52060 110 175 271 342 508 49580 80 140 220 270 330 395

100 60 100 160 210 260 305

Note: For lightweight concrete, the temperatures are reduced to 90% of thevalues given.

Heated lower side of slab

θcheff x

33



100

0

200

1000

1100

1200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90 100

Distance from exposed surface (mm)

Tem

pera

ture

(°C

)R30

R60

R90

R240

R180

Slab

200 mm thickR120

Fig. 4.7. Temperature profiles for slabs with height¼ 200mm

100

°C °C

200300400500

100

80

60

40

20

0

mm

0 20 40 60 80mm

b/h = 160/230 mm

100

200300400500

100

80

60

40

20

0

mm

0 20 40 60 80 100 120 140mm

b/h = 300/600 mm

t = 3

0 m

in

300

°C °C

400

500600700800

100

80

60

40

20

0

mm

0 20 40 60 80mm

100

200

300400500600700

100

80

60

40

20

0

mm

0 20 40 60 80 100 120 140mm

t = 6

0 m

in

500

°C °C

600

700800900

100

80

60

40

20

0

mm

0 20 40 60 80mm

200

300400500600700800900

100

80

60

40

20

0

mm

0 20 40 60 80 100 120 140mm

t = 9

0 m

in

500

°C °C

600

700

800900

100

80

60

40

20

0

mm

0 20 40 60 80mm

200

300400500600700800900

100

80

60

40

20

0

mm

0 20 40 60 80 100 120 140mm

t = 1

20 m

in

Fig. 4.8. Temperature profiles for beams with different width-to-height ratios

34



CHAPTER 5

Static loads

5.1. IntroductionAn accurate assessment of the performance of a structural member during a fire requires aknowledge of both the reduction in material properties at increasing temperature and anaccurate assessment of the loads acting on the structure at the time of the fire. Loadeffects have a significant impact during a fire and this is reflected in the requirement forrealistic load levels to be in place during standard fire tests. The importance of appliedload on fire resistance has long been recognized and was specifically incorporated into thecalculation models in the fire part of the British Standard for steel structures, BS 5950Part 8.12 The Eurocodes include load effects not only in relation to steel and compositestructures but also for concrete members. This is an important development as there is noexplicit allowance for the influence of applied load on the performance of concrete structuresin the National standard.

5.2. Partial safety factors for loadsThe calculation of the load effects at the fire limit state is different to the procedure adoptedin current National standards. The designer must be familiar with both EN 19906 (basis ofdesign) which provides the required load combinations (as for ambient temperature design)and with EN 1991-1-2 (the fire part of the Actions code) which in addition to specifying theavailable options for thermal actions for temperature analysis (see Chapter 3) also specifiesthe mechanical actions for structural analysis. In particular EN 1991-1-2 specifies the partialfactor for imposed (assuming leading variable action) loading for the fire limit state. Fireloading is an ultimate limit state accidental design situation (see EN 19906) of the form:

Ed ¼ EðGk; j;P;Ad; ð�1;1 or �2;1ÞQk;1; �2;iQk;iÞ for j � 1; i > 1 ð5:1Þwhere:

E is the effect of actions (Ed is the design value of the effect of actions);G is the permanent action (dead load);P is the relevant representative value of a prestressing action (where present);Ad is the design value of an accidental action;�1 is the factor for frequent value of a variable action;�2 is the factor for quasi-permanent value of a variable action; andQk is the characteristic value of a single variable action (Qk;1 is the characteristic value of

the leading variable action – often the imposed load).

In the fire situation Ad is the effect of the fire itself on the structure, i.e. the effects ofrestrained thermal expansion, thermal gradients, etc. However, EN 1991-1-2 states that:

Indirect actions from adjacent members need not be considered when fire safety require-ments refer to members under standard fire conditions.


And also that:

Imposed and constrained expansions and deformations caused by temperature changes due to fire

exposure results in effects of actions, e.g. forces and moments which shall be considered with theexception of those where they:

. May be recognised a priori to be negligible or favourable

. Are accounted for by conservatively chosen support models and boundary conditions and/or implicitlyconsidered by conservatively specified fire safety requirements.

EN 1990 allows the use of either �1 or �2 with the main variable action (generally theimposed load). EN 1991-1-2 recommends the use of �2; however, the UK NationalAnnex will specify the use of 1 as detailed in Table 5.1.

The benefits of this approach for concrete construction where the ratio of dead to imposedloads is relatively high (compared to typical steel-framed structures) are not particularlysignificant. The detailed calculations may be found in the worked examples section. Therelationship between the reduction factor and the ratio of the dead and imposed loads isillustrated in Fig. 5.1.

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.8

0.7

0.6

0.5

0.4

0.3

0.2

ψ1,1 = 0.9

ψ1,1 = 0.7

ψ1,1 = 0.5

ψ1,1 = 0.2

Qk,1/Gk

η fi

Fig. 5.1. Relationship between reduction factor �fi and ratio of dead and imposed loads for values of fi

5.3. Design values of loadsThe concept of reduced partial factors for the fire limit state will be explained using a designexample. The calculations are for the design of a column in a six-storey braced frame to resistthe loading applied from a 6m� 9m floor area. The design axial force in the column at thefire limit state is calculated using the appropriate partial factors.

Table 5.1. fi values for UK

Action �1 �2

Imposed loads in buildings:Category A: domestic, residentialCategory B: office areasCategory C: congregation areasCategory D: shopping areasCategory E: storage areasCategory F: traffic area �30 kNCategory G: traffic area 30–160 kNCategory H: roofs

0.50.50.70.70.90.70.50

0.30.30.60.60.80.60.30

Snow load: H � 1000m a.s.l. — 0

Wind loads on buildings 0.2 0

36



5.3.1. LoadingPermanent actions (G)Uniformly distributed load (UDL) over floor area Gk ¼ 2:00 kN/m2

Variable actions (Q)Uniformly distributed load (UDL) over floor area Qk ¼ 3:50 kN/m2

5.3.2. Ambient temperature design loadsLoad factorsPartial loading factor for permanent actions �G ¼ 1:35 (EN 1990 Table A1.2B and NA)Partial loading factor for variable actions �Q ¼ 1:50 (EN 1990 Table A1.2B and NA)

Design values of actions – ultimate limit stateArea UDL per floor W ¼ ð�GGkÞ þ ð�QQkÞ ¼ 7:95 kN/m2

Design axial force NEd ¼ 6m� 9m�W� 5¼ 2146.50 kN

5.3.3. Fire limit state design loadsFor the fire limit state, partial loading factors (�i) are not applied to either permanent actionsor variable actions.

Combination coefficient for variable action �1 ¼ 0:50. This is the value for offices using 1 ¼ 0:5 from Table 5.1.Note: EN 1990 allows use of either �1 or �2 with the main variable action. The NationalAnnex will specify which coefficient to use. EN 1991-1-2 recommends the use of �2;however, the UK National Annex will specify �1.

5.3.4. Design values of actions – ultimate limit state fire design situationArea UDL per floor W ¼ Gk þ ð�1QkÞ ¼ 3:75 kN/m2

Design axial force NEd ¼ 6m� 9m�W � 5 ¼ 1012:50 kN

5.4. Definition of load level, load intensity and degree ofutilizationDespite a slight difference in terminology between the different European standards, thebasic concept of load ratio, load level, load intensity or degree of utilization is the same.The resistance of the member at the fire limit state is assessed according to the amount ofload applied during a fire compared to the ambient temperature load-bearing capacity.The concept of load ratio is very useful with regard to tabulated data as it allows forgeneric solutions that cover a wide range of potential applications.

Throughout all the fire parts of the relevant Eurocodes the concept of a reduction factorfor the fire limit state is used, where:

Reduction factor �fi ¼ ðGk þ�fiQk1Þ=ð�GGk þ �Q;1Qk;1Þfor load combination (6.10) in EN 1990

In EN 1992-1-2 two factors related to the applied load are employed, namely load leveland degree of utilization. These are defined as follows.

5.4.1. Load level (n)This term is used to determine the fire resistance of reinforced concrete columns and relatesthe load imposed at the time of the fire to the ambient temperature load capacity.

n ¼ N0Ed;fi=½0:7ðAc fcd þ As fydÞ� ð5:2Þ

37

CHAPTER 5. STATIC LOADS


where:

N0Ed;fi is the axial load under fire conditions (kN);Ac is the area of concrete (mm2);fc;d is the concrete design compressive strength (N/mm2);As is the area of steel (mm2); andfyd is the steel design tensile strength (N/mm2).

The load imposed at the time of the fire is dependent on the choice of the partial factor forloading at the fire limit state. The choice of the partial factor is a Nationally DeterminedParameter (NDP) and is chosen at the discretion of the National body. The permissiblevalues are set out in EN 1990 and the choice is made in the National Annex to the firepart of EN 1991. For most common cases (domestic and office) the value of the partialfactor for imposed load will be 0.5, i.e. 0.5� the ambient temperature value. As a conserva-tive assumption when calculating the load level, N0Ed;fi may be taken as 0.7N0Ed (�fi ¼ 0:7)unless calculated explicitly.

5.4.2. Degree of utilization (�fi)This is the ratio of the load applied at the fire limit state to the load applied under ambientconditions and is dictated by the choice of partial factor for the fire limit state as discussedabove. It is used in the design of both columns and load-bearing walls.

�fi ¼NEd;fi

NRd

ð5:3Þ

where NEd;fi is the design axial load in the fire situation (kN) and NRd is the design resistanceof the column at normal temperature conditions (kN).

The reduction factor �fi may be used instead of �fi for the design load level as a conserva-tive assumption, as �fi assumes the member is fully loaded under ambient temperatureconditions. In EN 1994-1-2 the tabulated values are generally dependent on the load levelfor fire design �fi which can be explicitly calculated according to the formula above ortaken conservatively as 0.65.

38



CHAPTER 6

Thermal and mechanicalproperties of materials

6.1. IntroductionEN 1992-1-2, EN 1993-1-2 and EN 1994-1-2 provide guidance on the material properties ofhot-finished carbon steel, stainless steel, light gauged steel, normal-weight siliceous concrete,lightweight concrete, reinforcing steels, bolts and welds.

6.2. SteelHot-finished carbon steel begins to lose strength at temperatures above 3008C and reduces instrength at a steady rate up to 8008C. The small residual strength then reduces more gradu-ally until it reaches the melting temperature at around 15008C. This behaviour is similar forhot-rolled reinforcing steels. For cold-worked steels, including reinforcement, there is a morerapid decrease of strength after 3008C. In addition to the reduction of material strength andstiffness, steel displays a significant creep phenomenon at temperatures over 4508C.

High-temperature creep is dependent on the stress level and heating rate. The occurrenceof creep indicates that the stress and the temperature history have to be taken into account inestimating the strength and deformation behaviour of steel structures in fire. Including creepexplicitly within analytical models is complex. For the simple design methods presented inthe Eurocodes it is widely accepted that the effect of creep is implicitly considered in thestress–strain–temperature relationship.

Thermal and mechanical properties of different types of steel at elevated temperatures arediscussed. These include:

. hot-rolled carbon steel

. stainless steel

. light-gauged steel.

6.2.1. Hot-rolled carbon steelEN 1993-1-2 provides the material properties for hot-rolled steel of grades S235, S275 andS355 in accordance with EN 10025.

6.2.1.1. Thermal propertiesThe properties of thermal expansion, thermal conductivity and specific heat capacity of steelare dependent on steel temperature.

The coefficient of thermal elongation of steel �l=l can be determined by:

�l=l ¼ 1:2� 10�5�a þ 0:4� 10�8�2a � 2:416� 10�4 for 208C � �a < 7508C ð6:1aÞ


�l=l ¼ 1:1� 10�2 for 7508C � �a � 8608C ð6:1bÞ�l=l ¼ 2� 10�5�a � 6:2� 10�3 for 8608C < �a � 12008C ð6:1cÞ

where:

l is the length at 208C;�l is the temperature-induced elongation; and�a is the steel temperature (8C).

The variation of the thermal elongation with temperature is shown in Fig. 6.1.The specific heat of steel ca (in J/kgK) can be determined by:

ca ¼ 425þ 7:73� 10�1�a � 1:69� 10�3�2a

þ 2:22� 10�6�3a for 208C � �a < 6008C ð6:2aÞca ¼ 666þ 13 002=ð738� �aÞ for 6008C � �a < 7358C ð6:2bÞca ¼ 545þ 17 820=ð�a � 731Þ for 7358C � �a < 9008C ð6:2cÞca ¼ 650 for 9008C � �a � 12008C ð6:2dÞThe variation of the specific heat with temperature is shown in Fig. 6.2.The thermal conductivity of steel �a (in W/mK) can be determined by:

�a ¼ 54� 3:33� 10�2�a for 208C � �a < 8008C ð6:3aÞ�a ¼ 27:3 for 8008C � �a < 12008C ð6:3bÞThe variation of the thermal conductivity with temperature is shown in Fig. 6.3.

6.2.1.2. Mechanical propertiesThe stress–strain behaviour of carbon steel at high temperatures shows no clear yieldplateau, with strain hardening occurring throughout the plastic range. British Steel (nowCorus) carried out an extensive small-scale tensile transient test programme in the 1980son BS 4360: Grade 43A and Grade 50B steels to provide elevated temperature data for

12

16

20

0

4

8

0 200 400 600 800 1000 1200

Elo

ngat

ion Δ

l/l (

×10

–3)

θ (°C)

Fig. 6.1. Thermal elongation of carbon steel as a function of temperature

Spe

cific

hea

t (J/

kg K

)

0 200 400 600 800 1000 1200

θ (°C)

1000

0

2000

3000

4000

5000

Fig. 6.2. Specific heat of carbon steel as a function of temperature

40



structural fire engineering design applications. To represent the behaviour of beams andcolumns in standard fire tests, the heating rates were set at a range 5–208C/min.

The test results show that carbon steel begins to lose strength at temperatures above 3008Cand reduces in strength at a steady rate up to 8008C. The well-defined yield plateau at 208C isreplaced by a gradual increase of strength with increasing strain (or strain-hardening) at hightemperatures.

Based on the British Steel data, EN 1993-1.2 derives the reduction factors for effectiveyield strength, proportional limit and slope of linear elastic range as given in Table 6.1.The effective yield strength is related to 2% strain limit. Figure 6.4 illustrates the variationof the reduction factors with temperature.

The definitions of effective yield strength, proportional limit and slope of linear elasticrange are established on the basic characteristic of the stress–strain model for steel at hightemperatures given in EN 1993-1.2. Figure 6.5 shows that the first part of the curve is alinear line progressing up to the proportional limit fp;� and the elastic modulus Ea;� isequal to the slope of this straight-line segment. The second part of the curve depicts thetransition from the elastic to the plastic range. This region is formulated by an ellipticalprogression up to the effective yield strength fy;�. The third part of the curve is a flat yieldplateau up to a limiting strain. The last part of the curve is characterized by a linear linedecreasing to zero stress at the ultimate strain.

Comparing their reduction factors at elevated temperatures (Table 6.1), it can be seen thatthe stiffness of steel reduces more rapidly than the strength. This indicates that the failuremode of steel members may change at elevated temperatures. For instance, a steel beamcomprising a slender I-section, which is designed for plastic-hinge failure under ultimate

The

rmal

con

duct

ivity

(W

/m K

)

0 200 400 600 800 1000 1200

θ (°C)

10

0

20

30

40

50

60

Fig. 6.3. Thermal conductivity of carbon steel as a function of temperature

Table 6.1. Reduction factors for stress–strain relationship of steel at elevated temperatures

Steeltemperature�a (8C)

Reduction factor foreffective yield strengthky;� ¼ fy;�=fy

Reduction factor forproportional limitkp;� ¼ fp;�=fy

Reduction factor for the slopeof the linear elastic rangekE;� ¼ Ea;�=Ea

20 1.000 1.000 1.000100 1.000 1.000 1.000200 1.000 0.807 0.900300 1.000 0.613 0.800400 1.000 0.420 0.700500 0.780 0.360 0.600600 0.470 0.180 0.310700 0.230 0.075 0.130800 0.110 0.050 0.090900 0.060 0.0375 0.0675

1000 0.040 0.0250 0.04501100 0.020 0.0125 0.02251200 0.000 0.0000 0.0000

41

CHAPTER 6. THERMAL AND MECHANICAL PROPERTIES OF MATERIALS


load at ambient temperature, may experience the premature failure of web buckling atelevated temperatures.

EN 1993-1-2 provides detailed mathematical formulations for the stress–strain relation-ship of steel at elevated temperatures, as shown in Fig. 6.6.

The effect of creep is implicitly considered, with the material models being applicable forheating between 2 and 50K/min.

0.2

0

0.4

0.6

0.8

1.0

0 200 400 600 800 1000 1200

Temperature (°C)

Red

uctio

n fa

ctor

kp,θ

kE,θ ky,θ

Fig. 6.4. Reduction factors for stress–strain relationship of carbon steel at elevated temperatures

Strainεp,θ εy,θ εt,θ εu,θ

Stress σ

α

fy,θ

fp,θ

Ea,θ = tan α

Fig. 6.5. Stress–strain relationship for carbon steel at elevated temperatures

where: fy,θ is the effective yield strength at elevated temperatures; fp,θ is the proportional limit at elevated temperatures; Ea,θ is the slope of the linear elastic range at elevated temperatures; E is the slope of the linear elastic range at room temperature; εp,θ is the strain at the proportional limit at elevated temperatures; εy,θ is the yield strain at elevated temperatures; εt,θ is the limiting strain for yield strength at elevated temperatures; εu,θ is the ultimate strain at elevated temperatures.

Strain range

ε ≤ εp,θ εEa,θ Ea,θ

εy,θ ≤ ε ≤ εt,θ fy,θ 0

εt,θ < ε < εu,θ fy,θ[1 – (ε – εt,θ)/(εu,θ – εt,θ)] —

ε = εu,θ 0.00

Parameters εp,θ = fp,θ/Ea,θ

Functions a2 = (εy,θ – εp,θ)(εy,θ – εp,θ + c/Ea,θ)b2 = c(εy,θ – εp,θ)Ea,θ + c2

c = (fy,θ – fp,θ)2/[(εy,θ – εp,θ)Ea,θ) – 2(fy,θ – fp,θ)]

εy,θ = 0.02 εt,θ = 0.15 εu,θ = 0.20

—

εp,θ < ε < εy,θ

bfp,θ – c + √a2 – (εy,θ – ε)2

a

b(εy,θ – ε)

a √a2 – (εy,θ – ε)2

Stress σa (θa) Tangent modulus

Fig. 6.6. Mathematical formulations of stress–strain relationship for carbon steel at elevatedtemperatures

42



EN 1993-1-2 further extends the stress–strain relationship to include strain-hardeningfor steel temperatures below 4008C, provided local or overall buckling does not lead topremature collapse (Fig. 6.7). In this case, the mathematical formulations in Fig. 6.6 needto be modified as follows:

For 0:02 < " < 0:04:

�a ¼ 50ð fu;� � fy;�Þ"þ 2fy;� � fu;�

For 0:04 � " � 0:15:

�a ¼ fu;�

For 0:15 < " < 0:20:

�a ¼ fu;�½1� 20ð"� 0:15Þ�

For " � 0:20:

�a ¼ 0:0

where fu;� is the ultimate strength at elevated temperatures, allowing for strain-hardening.The ultimate strength at elevated temperatures fu;�, allowing for strain-hardening, shouldbe determined as follows:

For �a < 3008C:

fu;� ¼ 1:25fy;�

For 3008C � �a < 4008C:

fu;� ¼ fy;�ð2� 0:0025�aÞ

For �a � 4008C:

fu;� ¼ fy;�

Figure 6.8 shows the stress–strain relationships for S275 steel at elevated temperatures,allowing for strain hardening.

6.2.2. Stainless steelStainless steel covers a wide range of corrosion and heat-resistant iron-based materials,which contain at least 10% chromium, a maximum 1.2% carbon and other alloying ele-ments. There are five basic groups of stainless steel, classified according to their metallurgicalstructure, namely austenitic, ferritic, martensitic, duplex and precipitation-hardeninggroups. Austenitic and duplex stainless steels are the most widely used in architectural andstructural engineering applications, mainly due to their good weldability.

Annex C of EN 1993-1-2 provides guidance on the material properties, at elevatedtemperatures, for stainless steel Grades 1.4301, 1.4401, 1.4571, 1.4003 and 1.4462. Forother grades of stainless steel, the Code suggests that their mechanical properties may be

Strainεp,θ εy,θ εt,θεs,θ εu,θ

Stress σa

fu,θ

fy,θ

fp,θ

α

Ea,θ = tan α

Fig. 6.7. Stress–strain relationship for carbon steel at high temperatures allowing for strain hardening

43



taken as those for hot-rolled carbon steel, but the thermal properties are assumed to be thosefor general stainless steel.

6.2.2.1. Thermal propertiesThe thermal properties of stainless steel are quite different from those of carbon steel. Themain differences are as follows.

. The rate of thermal expansion of stainless steel remains relatively constant up to 12008Ccompared to carbon steel since stainless steel does not experience a phase transformation.

. The magnitude of thermal expansion of stainless steel is greater than the thermalexpansion of carbon steel.

. The specific heat of stainless steel increases slightly at elevated temperatures comparedto carbon steel, which has a huge increase in specific heat at 7308C due to a chemicaltransformation from ferrite-pearlite to austentite.

. At ambient temperature, stainless steel has a much lower thermal conductivity comparedto carbon steel. However, the thermal conductivity of stainless steel increases at elevatedtemperatures and exceeds the value for carbon steel above 10008C.

The thermal elongation of austenitic stainless steel �l=l may be determined by:

�l=l ¼ ð16þ 4:76� 10�3�a � 1:243� 10�6�2aÞ � ð�a � 20Þ � 10�6 ð6:4Þwhere:

l is the length at room temperature of stainless steel member;�l is the temperature-induced elongation of stainless steel member; and�a is the steel temperature (8C).

The variation of the thermal elongation with temperature is shown in Fig. 6.9.

100

150

0

50

200

250

300

350

Strain (%)0 2 4 6 8 10

20°C200°C250°C350°C400°C500°C600°C700°C

Str

ess

(N/m

m2 )

Fig. 6.8. Stress–strain relationships for S275 steel at elevated temperatures allowing for strain hardening

10

15

0

5

20

25

0 200 400 600 800 1000 1200

Carbon steelStainless steel

θ (°C)

Elo

ngat

ion

∆l/l

(×

10–3

)

Fig. 6.9. Thermal elongation of stainless steel as a function of temperature

44



The specific heat of stainless steel ca (in J/kgK) may be determined by:

ca ¼ 450þ 0:28� �a � 2:91� 10�4�2a þ 1:34� 10�7�3a ð6:5ÞThe variation of the specific heat with temperature is shown in Fig. 6.10.

The thermal conductivity of stainless steel �a (in W/mK) may be determined by:

�a ¼ 14:6þ 1:27� 10�2�a ð6:6ÞThe variation of the thermal conductivity with temperature is shown in Fig. 6.11.

6.2.2.2. Mechanical propertiesThe stress–strain relationship for stainless steel at elevated temperatures, given in EN 1993-1-2, is applicable for heating rates between 2 and 50K/min. The detailed mathematicalformulations are shown in Fig. 6.12.

Annex C of EN 1993-1-2 provides reduction factors, relative to the appropriate value at208C, for the stress–strain relationship of several grades of stainless steel at elevated tempera-tures as follows:

. Slope of linear elastic range, relative to slope at 208C: kE;� ¼ Ea;�=Ea

. Proof strength, relative to yield strength at 208C: k0:2p;� ¼ f0:2p;�=fy

. Tensile strength, relative to tensile strength at 208C: ku;� ¼ fu;�=fu

In addition, the Code gives a correction factor for the yield strength k2%;� for the useof simple calculation methods. It is assumed that the ‘effective’ yield strength to be used insimple calculation methods should be between the values of proof strength f0:2p;� andtensile strength fu as given by:

fy;� ¼ f0:2p;� þ k2%;�ð fu;� � f0:2p;�Þ ð6:7Þ

where the values of k2%;� for various grades of stainless steel, ranging from 0.19 to 0.47, aregiven in Annex C of EN 1993-1-2.

Table 6.2 and Fig. 6.13 illustrate the variation of the above-mentioned reduction factorsfor Grade 1.4301 stainless steel. Annex C of EN 1993-1-2 provides values for other gradesof stainless steel.


0 200 400 600 800 1000 1200θ (°C)

1000

0

2000

3000

4000

5000

Spe

cific

hea

t (J/

kg K

)

Fig. 6.10. Specific heat of stainless steel as a function of temperature


0 200 400 600 800 1000 1200

10

0

20

30

40

50

60

The

rmal

con

duct

ivity

(W

/m K

)

θ (°C)

Fig. 6.11. Thermal conductivity of stainless steel as a function of temperature

45



Stress σ

α

α

fu,θ

f0.2p,θ

Ect,θ = tan α

where: fu,θ is the tensile strength; f0.2p,θ is the proof strength at 0.2% plastic strain; Ea,θ is the slope of the linear elastic range; Ect,θ is the slope of proof strength; εc,θ is the total strain at proof strength; εu,θ is the ultimate strain.

Strain range

ε ≤ εc,θ Eε

1 + aεb

E(1 + aεb – abεb)

(1 + aεb)2

Parameters εc,θ = f0.2p,θ/Ea,θ + 0.02

d2 = e(εu,θ – εc,θ)Ect,θ + e2

εc,θ < ε < εu,θ

df0.2p,θ – e + √c2 – (εu,θ – ε)2

c

Functions Ea,θεc,θ – f0.2p,θa = f0.2p,θεc

b,θ

(1 – εc,θEct,θ/f0.2p,θ)Ea,θεc,θb = (Ea,θεc,θ/f0.2p,θ – 1)f0.2p,θ

d + (εu,θ – ε)

c √c2 – (εu,θ – ε)2

Stress σ Tangent modulus Et

(fu,θ – /f0.2p,θ)2

e = (εu,θ – εc,θ)Ect,θ – 2(fu,θ – f0.2p,θ)

ec2 = (εu,θ – εc,θ) (εu,θ – εc,θ + ) Ect,θ

Strain εu,θεc,θ

Fig. 6.12. Stress–strain relationship for stainless steel at elevated temperatures

Table 6.2. Parameters for stress–strain relationship of stainless steel Grade1.4301 at elevated temperatures

�a (8C) Ea;�=Ea f0:2p;�=fy fu;�=fu k2%;�

20 1.00 1.00 1.00 0.26100 0.96 0.82 0.87 0.24200 0.92 0.68 0.77 0.19300 0.88 0.64 0.73 0.19400 0.84 0.60 0.72 0.19500 0.80 0.54 0.67 0.19600 0.76 0.49 0.58 0.22700 0.71 0.40 0.43 0.26800 0.63 0.27 0.27 0.35900 0.45 0.14 0.15 0.381000 0.20 0.06 0.07 0.401100 0.10 0.03 0.03 0.401200 0.00 0.00 0.00 0.40

46



6.2.3. Light-gauge steelLight-gauge steel sections can be produced in a large variety of sections and profiled sheeting.Traditionally, in building construction, the commonly used sections are cold-formed ‘C’ or‘Z’ shapes used as roof purlins and side rails to support the cladding in industrial buildings.More recently, light-gauge sections have been widely used as steel frames, trusses, wallpartitions, lintels, floor joists and storage racking.

The main advantage of light-gauge sections is the high strength-to-weight ratio at ambienttemperature. For cold-formed sections, the strain-hardening caused by the cold-workingprocess increases the yield strength and ultimate strength of the materials. However, thesecharacteristics make them more vulnerable to fire exposure. Light-gauge sections havelittle fire resistance because they heat up quickly if directly exposed to fire due to theirhigh section factors. The increase of mechanical strength due to strain-hardening will alsobe removed quickly during heating.

Although widely used in the UK, the performance of light-gauge steel in fire is only brieflydescribed in the Eurocodes.

6.2.3.1. Thermal propertiesThe thermal properties of light-gauged steel should be assumed to be similar to the thermalproperties of hot-rolled steel.

6.2.3.2. Mechanical propertiesAnnex E of EN 1993-1-2 provides reduction factors for the design strength and elasticmodulus of Class 4 sections made of carbon steel at elevated temperatures as shown inTable 6.3 and Fig. 6.14, which can be used for light-gauge sections.

Elastic modulusProof strengthTensile strength

Stainless steel Grade 1.4301

0 200 400 600 800 1000 1200Temperature (°C)

Red

uctio

n fa

ctor

1.0

0.8

0.6

0.4

0.2

0

Fig. 6.13. Reduction factors for stress–strain relationship of stainless steel grade 1.4301 at elevatedtemperatures

Table 6.3. Reduction factors for carbon steel for Class 4 sections at elevated temperatures

Steeltemperature�a (8C)

Reduction factor forthe design strengthkp0:2;�

Reduction factor for the slopeof the linear elastic rangekE;� ¼ Ea;�=Ea

20 1.00 1.00100 1.00 1.00200 0.89 0.90300 0.78 0.80400 0.65 0.70500 0.53 0.60600 0.30 0.31700 0.13 0.13800 0.07 0.09900 0.05 0.071000 0.03 0.051100 0.02 0.021200 0.00 0.00

47



For simplicity, EN 1993-1-2 conservatively adopts 0.2% proof stress as the effective yieldstrength for the design of Class 4 steel sections at elevated temperatures. For hot-rolled andwelded thin-walled sections, the reduction factor for the design strength kp0:2;� is takenrelative to the yield strength at 208C fy as follows:

kp0:2;� ¼ fp0:2;�=fy

where fp0:2;� is the 0.2% proof strength at steel temperature �a taken as the effective yieldvalue.

For cold-formed light-gauge sections, the reduction factor for the design strength kp0:2;� istaken relative to the basic yield strength at 208C fyb as follows:

kp0:2;� ¼fp0:2;�

fyb

where fyb is the basic yield strength as defined in EN 1993-1-3.The reduction factor for elastic modulus is assumed to be identical to that of carbon steel.

6.3. ConcreteConcrete is a non-homogeneous material whose fire performance is controlled by that of theaggregate and the cement paste. Concretes are conventionally grouped as normal-weightconcrete and lightweight concrete, depending on the density of the aggregates used.EN 1994 does not cover the design of composite structures with concrete strength classeslower than C20/25 and LC20/25 and higher than C60/75 and LC60/75. For strengthshigher than C60/75 guidance is provided in EN 1992-1-2.

Concrete has a low thermal conductivity (50 times lower than steel) and therefore heats upvery slowly in a fire. It is the low thermal conductivity that provides good inherent fireresistance of concrete structures.

EN 1994-1-2 provides material properties for normal-weight siliceous concrete and light-weight concrete. For calcareous concrete material properties either the siliceous concreteproperties can, conservatively, be used or reference made to EN 1992-1-2.

6.3.1. Normal-weight concreteThis section provides the thermal and mechanical properties of normal-weight concrete withsiliceous or calcareous aggregates in accordance with EN 1992-1-223. The concrete strengthclasses range from C12/15 to C50/60. The strength classification of C12/15 refers to aconcrete grade with characteristic cylinder and cube strength of 12N/mm2 and 15N/mm2

respectively.

6.3.1.1. Thermal propertiesEN 1992-1-2 and EN 1994-1-2 provide the following models incorporating temperatureeffects for the thermal properties of normal-weight concrete.

0 200 400 600 800 1000 1200Temperature (°C)

Slope of linear elastic rangeDesign strength

Red

uctio

n fa

ctor

1.0

0.8

0.6

0.4

0.2

0

Fig. 6.14. Strength reduction factors for cold-worked steel at elevated temperatures

48



The thermal strain (expansion) of concrete "c;� can be determined by:

For siliceous aggregates:

"c;� ¼�1:8� 10�4 þ 9� 10�6�þ 2:3� 10�11�3 for 208C � �c � 7008C

14� 10�3 for 7008C < �c � 12008C

(ð6:8aÞ

For calcareous aggregates:

"c;� ¼�1:2� 10�4 þ 6� 10�6�þ 1:4� 10�11�3 for 208C � �c � 8058C

12� 10�3 for 8058C < �c � 12008C

(ð6:8bÞ

where �c is the concrete temperature (8C).The variation of the thermal elongation with temperature is shown in Fig. 6.15.The specific heat of dry concrete cc;� (in J/kgK) (i.e. moisture content by weight u ¼ 0%)

can be determined by:

For siliceous and calcareous aggregates:

"c;� ¼

900 for 208C � �c � 1008C

900þ ð�� 100Þ for 1008C < �c � 2008C

1000þ ð�� 200Þ=2 for 2008C < �c � 4008C

1100 for 4008C < �c � 12008C

8>>><>>>:

ð6:9Þ

The variation of the specific heat with temperature is shown in Fig. 6.16.Where the moisture content u is not considered explicitly in analysis, the specific heat of

concrete may be modelled by peak value at 1158C as given below:

c�c ¼1470 for u ¼ 1:5%

2020 for u ¼ 3:0%

5600 for u ¼ 10:0%

8><>: ð6:10Þ

0 200 400 600 800 1000 1200Temperature (°C)

The

rmal

str

ain

(×10

–3)

16

14

12

10

8

6

4

2

0

Normal weight concrete –siliceous & high strength

Normal weight concrete –

calcareous & high strength

Light weight concrete

Fig. 6.15. Thermal strains of concrete at elevated temperatures

NWC (u = 1.5%)

NWC (u = 0%)

NWC (u = 3%)

LWC

2.5

2.0

1.5

1.0

0.5

0

Spe

cific

hea

t (kJ

/kg

K)

0 200 400 600 800 1000 1200Temperature (°C)

Fig. 6.16. Specific heat of concretes at elevated temperatures

49



The value of u ¼ 10:0% may occur for hollow sections filled with concrete. For othermoisture contents, linear interpolation between the above given values is acceptable. Thepeak values of specific heat are shown in Fig. 6.16.

The variation of density of concrete �c;� with temperature is influenced by free water lossand is defined as follows:

�c;� ¼

�c;20 for 208C � �c � 1158C

�c;20½1� 0:02ð�� 115Þ=85� for 1158C < �c � 2008C

�c;20½0:98� 0:03ð�� 200Þ=200� for 2008C < �c � 4008C

�c;20½0:95� 0:07ð�� 400Þ=800� for 4008C < �c � 12008C

8>>><>>>:

ð6:11Þ

where �c;20 is concrete density at ambient temperature.The variation of the ratio of �c;� to �c;20 with respect to temperature is shown in Fig. 6.17.The thermal conductivity of concrete �c (in W/mK), for 208C � �c � 12008C, can be

determined between the lower and upper limit values as follows:

�c ¼2� 0:2451ð�c=100Þ þ 0:0107ð�c=100Þ2 for upper limit

1:36� 0:136ð�c=100Þ þ 0:0057ð�c=100Þ2 for lower limit

(ð6:12Þ

The variation of the upper limit and lower limit of thermal conductivity with temperature isshown in Fig. 6.18.

6.3.1.2. Mechanical propertiesFigure 6.19 illustrates the stress–strain relationship model for concrete under uniaxialcompression at elevated temperatures in accordance with EN 1992-1-223, with the valuesfor each of these parameters as a function of concrete temperatures given in Table 6.4.

Figure 6.20 shows the corresponding reduction in strength for normal weight and light-weight concrete. Figure 6.21 shows the typical stress–strain curves for normal-weight

1.00

0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

ρ c,θ /ρ

c,20

0 200 400 600 800 1000 1200Temperature (°C)

Fig. 6.17. Density of concrete at elevated temperatures

Normal weight concrete &high strength concrete – upper limit

Normal weight concrete &high strength concrete – lower limit


The

rmal

con

duct

ivity

(W

/m K

) 2.0

1.6

1.2

0.8

0.4

00 200 400 600 800 1000 1200

Temperature (°C)

Fig. 6.18. Thermal conductivity of concretes at elevated temperatures

50



concrete at elevated temperatures in accordance with the mathematical model given inFig. 6.19. It can be seen that the peak compressive strength fc;� reduces and the correspondingstrain increases with increasing temperature.

Conservatively, the tensile strength of concrete can be ignored. However, EN 1992-1-2allows the tensile strength to be taken into account. The reduction of the characteristictensile strength of concrete is governed by the coefficient kc;t(�) as given by:

fck;tð�Þ ¼ kc;tð�Þ fck;t ð6:13Þ

Linear or non-linear models

3εfc,θ for ε ≤ εc1,θεc1,θ[2 + (ε/εc1,θ)

3]

for εc1,θ < ε ≤ εcu1,θ

σ(θ) =

⎧⎪⎪⎨⎪⎪⎩

Strain ε

Str

ess

σ

εc1,θ εcu1,θ

fc,θ

Fig. 6.19. Stress–strain relationship of concrete under compression at elevated temperatures

Table 6.4. Parameters for stress–strain relationship of normal-weight and lightweight concrete atelevated temperatures

TemperatureSiliceous NWC Calcareous NWC LWC

� (8C) fc;�=fck "c1;� "cu1;� fc;�=fck "c1;� "cu1;� fc;�=fck "c1;� and "cu1;�

20 1.00 0.0025 0.0200 1.00 0.0025 0.0200 1.00 Obtained100 1.00 0.0040 0.0225 1.00 0.0040 0.0225 1.00 from tests200 0.95 0.0055 0.0250 0.97 0.0055 0.0250 1.00300 0.85 0.0070 0.0275 0.91 0.0070 0.0275 1.00400 0.75 0.0100 0.0300 0.85 0.0100 0.0300 0.88500 0.60 0.0150 0.0325 0.74 0.0150 0.0325 0.76600 0.45 0.0250 0.0350 0.60 0.0250 0.0350 0.64700 0.30 0.0250 0.0375 0.43 0.0250 0.0375 0.52800 0.15 0.0250 0.0400 0.27 0.0250 0.0400 0.40900 0.08 0.0250 0.0425 0.15 0.0250 0.0425 0.28

1000 0.04 0.0250 0.0450 0.06 0.0250 0.0450 0.161100 0.01 0.0250 0.0475 0.02 0.0250 0.0475 0.041200 0.00 — — 0.00 — — 0.00

Nornal weight concrete –calcareous

Nornal weight concrete –siliceous


Red

uctio

n fa

ctor

of s

tren

gth 1.0

0.8

0.6

0.4

0.2

00 200 400 600 800 1000 1200

Temperature (°C)

Fig. 6.20. Reduction in strength for normal- and lightweight concretes at elevated temperatures

51



with

kc;tð�Þ ¼1:0 for 208C � � � 1008C

1:0� 1:0ð�� 100Þ=500 for 1008C < � � 6008C

�

where fck;t is the concrete characteristic tensile strength (N/mm2).

6.3.2. Lightweight concreteThis section provides the thermal and mechanical properties of lightweight concrete (LWC)in accordance with EN 1994-1-2. The density of unreinforced lightweight concrete consid-ered in this code shall be in the range 1600–2000 kg/m3.

6.3.2.1. Thermal propertiesLightweight concrete has very good thermal properties with half the thermal expansion andthermal conductivity of normal-weight concrete. EN 1994-1-2 provides the following modelsfor the thermal properties of lightweight concrete.

The related thermal elongation �l=l of lightweight concrete may be determined from:

�l=l ¼ 8� 10�6ð�c � 20Þ ð6:14Þwhere:

l is the length at room temperature of lightweight concrete member;�l is the temperature-induced elongation of lightweight concrete member; and�c is the concrete temperature (8C).

The variation of the thermal elongation with temperature is shown in Fig. 6.15. Thespecific heat cc (in J/kgK) of lightweight concrete may be considered to be independent ofthe concrete temperature:

cc ¼ 840

The value of specific heat of lightweight concrete is shown in Fig. 6.16. The thermal con-ductivity �c (in W/mK) of lightweight concrete may be determined from the following:

�c ¼1:0� ð�c=1600Þ for 208C � �c � 8008C

0:5 for �c > 8008C

�ð6:15Þ

The variation of the thermal conductivity with temperature of lightweight concrete isshown in Fig. 6.18.

6.3.2.2. Mechanical propertiesEN 1994-1-2 adopts the same stress–strain relationship model for lightweight concrete asnormal-weight concrete. The model is given in Fig. 6.19 and Table 6.4. However, the codeonly provides the values for the reduction of strength kc;� ¼ fc;�=fck as shown in Table 6.4.The values of the strain corresponding to fc;� should be obtained from tests. The strength

20

800

200

400

1000

600

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5Strain (%)

Rel

ativ

e co

mpr

essi

ve s

tren

gth 1.0

0.8

0.6

0.4

0.2

0

Fig. 6.21. Stress–strain curves for siliceous concrete at elevated temperatures

52



reduction factor of lightweight concrete is compared to that of normal-weight concrete inFig. 6.20. Lightweight concrete has better strength retention than normal-weight concrete.

6.3.3. High-strength concreteThe strength of normal-weight concrete (NWC) is typically limited by the strength of thecement matrix. It is commonly known that concrete compressive strength is inverselyrelated to the water–cement ratio. The advance of material technology and productionhas led to higher grades of concrete, ranging from 50 to 130MPa. High-strength concrete(HSC) is mainly achieved by either adding water-reducing admixtures to obtain a lowwater–cement ratio, or adding silica fume. Consequently, HSC has lower permeability andwater content compared with NWC.

HSC provides superior structural properties including higher strength, higher stiffness andbetter durability. Hence, HSC is usually considered as a high-performance constructionmaterial, and HSC structural elements have been widely used in construction projectsaround the world, including bridges, high-rise buildings and special structures.

Since the 1980s, many fire tests have been conducted to investigate the material propertiesof HSC at elevated temperatures. The test results37�39 have generally identified the two maindifferences in the behaviour of HSC at high temperatures from that of normal-strengthconcrete:

(1) The strength loss of HSC at elevated temperatures is more pronounced.(2) The susceptibility of HSC to explosive spalling at temperatures below 4008C.

With the exception of these two points, it is commonly suggested that HSC can be treated asconventional, normal-strength concrete in the fire engineering design. This hypothesis hasbeen adopted in the Eurocodes.

This section provides the thermal and mechanical properties of HSC in accordance withEN 1992-1-2. The code divides high-strength concrete into three classes, namely:

(1) Class 1 for concrete C55/67 and C60/75(2) Class 2 for concrete C70/85 and C80/95(3) Class 3 for concrete C90/105.

The strength notation of C55/67 refers to a concrete grade with characteristic cylinder andcube strength of 55N/mm2 and 67N/mm2, respectively.

Table 6.5. Reduction in strength for high-strength concrete at elevated temperatures

Concretetemperature

fc;�=fck

� (8C) Class 1 Class 2 Class 3

20 1.00 1.00 1.0050 1.00 1.00 1.00100 0.90 0.75 0.75200 0.90 0.75 0.70250 0.90 0.75 0.675300 0.85 0.75 0.65400 0.75 0.75 0.45500 0.60 0.60 0.30600 0.45 0.45 0.25700 0.30 0.30 0.20800 0.15 0.15 0.15900 0.08 0.113 0.081000 0.04 0.075 0.041100 0.01 0.038 0.011200 0.00 0.00 0.00

53



6.3.3.1. Thermal propertiesEN 1992-1-2 assumes that HSC has the same thermal properties as NWC. However, it isnoteworthy that the actual thermal conductivity of HSC may be higher than that for NWC.

6.3.3.2. Mechanical propertiesBased on a limited number of test results, EN 1992-1-2 provides the reduction of strengthfc;�=fck of HSC at elevated temperatures as shown in Table 6.5 and Fig. 6.22. Comparedto normal-weight concrete with siliceous aggregate, HSC generally suffers greater strengthreduction at high temperatures, in particular at low temperatures below 3008C.

6.4. Reinforcing steelEN 1994-1-2 covers hot-rolled and cold-worked reinforcing steel. It is assumed that pre-stressing steel will not be used in composite structures.

The thermal and mechanical properties of hot-rolled reinforcing steel are assumed to bethe same as hot-rolled steel, covered in Section 6.2.1. For cold-worked reinforcing steelthe thermal properties are assumed to be the same as hot-rolled steel but the mechanicalproperties vary. The three main parameters for cold-worked reinforcing steel representingthe stiffness, extent of the proportional limit, and the yield strength, for a given temperature,are shown in Table 6.6. The values are represented as reduction factors based on values atambient temperature.

HSC – Class 1HSC – Class 2HSC – Class 3NWC – siliceous

0 200 400 600 800 1000 1200Temperature (°C)

Red

uctio

n fa

ctor

of s

tren

gth

1.0

0.8

0.6

0.4

0.2

0

Fig. 6.22. Reduction in strength for high-strength concrete at elevated temperatures

Table 6.6. Reduction factors for cold-worked reinforcing steel

Steeltemperature�s (8C)

Reduction factor foreffective yield strengthEs�=Es

Reduction factor forproportional limitfsp;�=fsy

Reduction factor foreffective yield strengthfsy;�=fsy

20 1.00 1.00 1.00100 1.00 0.96 1.00200 0.87 0.92 1.00300 0.72 0.81 1.00400 0.56 0.63 0.94500 0.40 0.44 0.67600 0.24 0.26 0.40700 0.08 0.08 0.12800 0.06 0.06 0.11900 0.05 0.05 0.081000 0.03 0.03 0.051100 0.02 0.02 0.031200 0.00 0.00 0.00

54



6.5. Bolts and weldsAnnex D of EN 1993-1-2 provides limited information on the fire performance of bolts andwelds, comprising mechanical properties with varying temperature relative to the adjoiningbeam. For bolted connections, EN 1993-1-2 states that net-section failure at fastener holesneed not be considered, provided that there is a fastener in each hole, since it is assumedthat the steel temperature is normally lower at connections due to the presence of additionalmaterial.

Based on a limited number of tests, the code assigns the same strength reduction factor kb;�for bolts in shear and tension, regardless of bolt types. For friction grip bolts, it is assumedthat the bolts slip in fire and the fire resistance of a single bolt may be designed for shear andbearing.

The fire design resistance for bolts should be determined from the following:

For shear resistance:

Fv;t;Rd ¼ Fv;Rdkb;��M2

�M;fi

For bearing resistance:

Fb;t;Rd ¼ Fb;Rdkb;��M2

�M;fi

For tension resistance:

Ften;t;Rd ¼ Ft;Rdkb;��M2

�M;fi

where:

Fb;Rd is the design bearing resistance according to EN 1993-1.8;Ft;Rd is the design tension resistance according to EN 1993-1.8;Fv;Rd is the design shear resistance of the bolt according to EN 1993-1-8;kb;� is the reduction factor for appropriate bolt temperature from Table 6.7;�M2 is the partial safety factor at normal temperature; and�M;fi is the partial safety factor for fire conditions.

The variation of the strength reduction factor is illustrated in Fig. 6.23.The design strength of a full penetration butt weld, for temperatures up to 7008C, should

be taken as equal to the strength of the connecting members using the appropriate reductionfactors for structural steel. For temperatures greater than 7008C, the reduction factors givenfor fillet welds can also be applied to butt welds.

Table 6.7. Strength reduction factors for bolts and welds

Temperature� (8C)

Bolts in shearand tensionkb;�

Fillet weldskw;�

Butt weldskw;�

20 1.000 1.000 1.000100 0.968 1.000 1.000200 0.935 1.000 1.000300 0.903 1.000 1.000400 0.775 0.876 1.000500 0.550 0.627 0.780600 0.220 0.379 0.470700 0.100 0.130 0.230800 0.067 0.074 0.074900 0.033 0.018 0.0181000 0.000 0.000 0.000

55



The design resistance per unit length of a fillet weld in fire should be determined from:

Fw;t;Rd ¼ Fw;Rdkw;��M2

�M;fi

where:

Fw;Rd is the design weld resistance per unit length according to EN 1993-1-8; andkw;� is the reduction factor for appropriate weld temperature from Table 6.7.

The variation of strength reduction factor is illustrated in Fig. 6.23. Fillet welds areconsidered to have better fire performance than bolts, but have a lower strength retentioncompared to butt welds or the parent metal.

BoltsFillet weldsButt weldsCarbon steel

kb,θ

kw,θ

0 200 400 600 800 1000 1200Temperature (°C)

Red

uctio

n fa

ctor

1.0

0.8

0.6

0.4

0.2

0

Fig. 6.23. Strength reduction factors for bolts and welds at elevated temperatures

56



CHAPTER 7

Design of tension members

7.1. IntroductionThis chapter gives guidance on the design of steel tension members. Tension members can beused in many applications, some of which are detailed below.

. Single angles, tees, channels and structural hollow sections are used in light trusses andlattice girders.

. Single sections, compound sections consisting of double angles or channels and bars andflats are used as bracing members in buildings.

. Ropes and cables are used as main cables and deck suspension cables in cable-stayedstructures and suspension bridges.

. Heavy rolled sections and heavy compound sections of built-up H and box sections areused as the hangers in suspended structures.

Typical section types and examples of where tension members are used in buildings andbridges are given in Figs 7.1 and 7.2 respectively.

EN 1993: Part 1.2 permits two methods of assessing the fire resistance of steel members intension. The first, the ‘design resistance’ method, consists of calculating the design resistanceof a member based on the distribution of temperature through its cross-section, the area ofthe cross-section and its reduced material properties at elevated temperature. The second, the‘critical temperature’ method, consists of calculating the temperature at which the memberwill fail, assuming a uniform temperature distribution and a given degree of utilization.Both methods are explained in the next sections.

Bars

Fig. 7.1. Typical sections used as tension members

7.2. Design resistance methodEN 1993: Part 1.2 gives two approaches for calculating the design resistance of a tensionmember at elevated temperature. The first approach can be used for a tension member with


a non-uniform temperature distribution across its cross-section, while the second is for atensionmember with a uniform temperature distribution across its cross-section. Alternatively,the design resistance of a tension member with a non-uniform temperature distribution acrossits cross-section can be conservatively taken as equal to the design resistance of a member witha uniform temperature distribution provided the uniform temperature taken is equal to themaximum temperature in the section with a non-uniform distribution.

7.2.1. Non-uniform temperature distributionEN 1993: Part 1.2 gives the design resistance, Nfi;t;Rd, at time, t, of a tension member with anon-uniform temperature distribution across its cross-section as:

Nfi;t;Rd ¼Xni¼1

Aiky;�;i fy=�M;fi ð7:1Þ

where:

Ai is an elemental area of the cross-section with a temperature �i;ky;�;i is the reduction factor for the yield strength of steel at temperature �i;�i is the temperature in the elemental area Ai;fy is the yield strength at 208C; and�M;fi is the partial factor for the relevant material property for the fire situation.

Tie

Tie

Hangers

Fig. 7.2. Tension members in buildings and bridges

58



In this method the cross-section is divided into a number of discrete elements and the area,temperature, reduction factor and yield strength for each element determined. The aboveequation is then used to sum together the resistances of each of the individual elements toobtain the resistance of the complete cross-section. Any convenient subdivision may beused but for accurate results the section should be divided into elements that have anapproximately uniform temperature distribution. Where the temperature distributionvaries over the area of the element, the highest temperature should be used.

A worked example follows.

Example 7.1: Tension resistance of equal angleIt is required to calculate the tension resistance of the tensionmember shown in Fig. 7.3(a).The temperature distribution is non-uniform over the cross-section, varying linearly from6008C at the bottom of the angle to 2008C at the top of the angle.

Section size and material propertiesSection size: 100� 100� 15mm equal angleSteel grade: S275

Calculation procedureThe angle can be conveniently subdivided into its vertical and horizontal legs, as shown inFig. 7.3(b). The maximum temperature in each of these elements is 6008C and 5408Crespectively.

The tension resistance of element 1 can be calculated as follows:

Nfi;t;Rd;1 ¼ A1ky;�;1 fy1=�M;fi;1

200°C

600°C

100(a)

100

15

2

1

200°C

600°C540°C

(b)

85

(c)

3

2

1

200°C

600°C540°C

370°C

42.5

42.5

Fig. 7.3. Tension member subject to non-uniform temperature distribution: (a) non-uniformtemperature distribution; (b) maximum temperature in each leg; and (c) subdividing vertical leg. (Alldimensions in mm)

59

CHAPTER 7. DESIGN OF TENSION MEMBERS


7.2.2. Uniform temperature distributionEN 1993-1-2 gives the design resistance, Nfi;t;Rd, of a tension member with a uniform tem-perature �a across its cross-section as:

Nfi;t;Rd ¼ ky�NRdð�M;1=�M;fiÞ ð7:2Þ

where:

ky� is the reduction factor for the yield strength of steel at temperature, �a; andNRd is the design resistance of the gross cross-section Npl;Rd for normal temperature

design according to EN 1993-1-1.

This method is based on the design method for tension members at the cold conditiongiven EN 1993: Part 1.1 but introduces a reduction factor ky� to account for the reductionin the material properties at elevated temperature. However, there is one key differencebetween this approach and that used for cold designs and it concerns the performance ofthe member at net sections. In the fire condition it is assumed that at a bolt hole, providedthe hole is filled with a bolt, the section around the hole will not be heated to the sameextent as the rest of the member. This is because locally the thermal mass is increased dueto the presence of the bolt. The result of this effect is to increase the resistance of themember at its net section to such an extent that gross section properties can be used inplace of the net section properties.

7.3. Critical temperature methodThe critical temperature, �a;cr, for a steel tension member at time, t, with a uniform tempera-ture distribution is the temperature at which the capacity of the member is reduced to theapplied load. In EN 1993 the critical temperature may be determined for any degree ofutilization from the following expression:

�a;cr ¼ 39:19 ln

�1

0:9674�3:833o

� 1

�þ 482 ð7:3Þ

where:

�o is the degree of utilization in the member and is given by the following expression:

�o ¼ Efi;d=Rfi;d;0 ð7:4Þ

Substituting the values for A1, ky;�;1, fy1 and �M;fi;1 for element number 1 gives thefollowing result for its tension resistance:

Nfi;t;Rd;1 ¼ 100� 15� 0:470� 275=1:0=1000 ¼ 193:9 kN

The tension resistance of element number 2 can be found in the same way and gives atension resistance of 241 kN. The tension resistance of the member can then be determinedby adding together the tension resistances of each of the two elements.

Nfi;t;Rd ¼ Nfi;t;Rd;1 þNfi;t;Rd;2

The design tension resistance for this member is therefore:

Nfi;t;Rd ¼ 193:9þ 241 ¼ 435 kN

Alternatively, a more accurate assessment of the tension resistance of the member can bedetermined by subdividing the vertical leg of the angle into two elements as shown inFig. 7.3(c), thus dividing the cross-section into three elements. The maximum temperatureof elements 1, 2 and 3 are 6008C, 5408C and 3708C respectively. By following the aboveprocedure it can easily be shown that the new tension resistance of the members is490 kN. This represents a 12% improvement on the previous value.

60



where:

Rfi;d;0 is the value of Rfi;d;t for time t ¼ 0 (i.e. in the cold condition);Rfi;d;t is as given in Chapter 5 of this handbook; andEfi;d is as given in Chapter 5 of this handbook.

The degree of utilization can be defined as the ratio of applied load at the fire Limit State(Efi;d) to the capacity of the member under normal conditions (Rfi;d;0). For tension membersthe capacity at fire time t ¼ 0 can be taken as its ambient temperature capacity. The capacityof a tension member at ambient temperature can be determined from the appropriateexpression given in EN 1993: Part 1.1.

Alternatively, for tension members �o may be conservatively obtained from the followingexpression:

�o ¼ �fið�M;fi=�M;1Þ ð7:5Þ

where:

�fi is the reduction factor as given in Chapter 5 of this handbook.

This method assumes that the member has been designed to its full strength at the coldcondition and therefore the utilization factor may be calculated from a ratio of theapplied load at the fire Limit State to the ultimate design load at the ambient condition. Ifthe structure is subject to a combination of dead load (G) and imposed load (Q), the utiliza-tion factor can therefore be expressed in the following form:

�o ¼Gþ Q

1:35Gþ 1:5Qð�M;fi=�M;1Þ

where is the combination factor for the imposed load under fire conditions and the factors1.35 and 1.5 are the partial safety factors for dead load and imposed load.

Table 7.1 compares the temperatures predicted by the critical temperature method ofEN 1993-1-2 with those from BS 5950: Part 812 for tension members. Form this table itcan be seen that the critical temperature method gives very similar results to the limiting tem-perature, load-ratio method given in BS 5950: Part 8.


Table 7.1. Comparison of the critical temperature method in EN 1993 with the limiting temperaturemethod of BS 5950: Part 8

Critical/limiting temperatures at a utilization (load ratio) of:

Method 0.7 0.6 0.5 0.4 0.3 0.2

BS 5950: Part 8 460 510 545 590 635 690EN 1993 526 554 585 620 664 725

Example 7.2: Calculation of critical temperatureIn this example calculate the critical temperature for the single angle in the previousworked example, assuming the member has an applied load of 500 kN.

The tension resistance at time t ¼ 0 is Rfi;d;0 ¼ 2800� 275=1000 ¼ 770 kN. Thereforethe utilization factor is �o ¼ 500=770 ¼ 0:649. From equation (7.3) the critical tempera-ture of the member is 5408C.

61

CHAPTER 7. DESIGN OF TENSION MEMBERS


CHAPTER 8

Design of compressionmembers

8.1. IntroductionThis chapter gives guidance on the design of members subjected mainly to compression(hereafter to be referred to as columns). It will consider steel, composite and reinforcedconcrete columns.

In the various Eurocodes, the aim of the design calculations is to ensure that a structuralmember has sufficient load-carrying capacity at elevated temperatures to resist the appliedload in the structural member at the fire limit state, this design philosophy being identicalto that at ambient temperature. Therefore, temperatures in the structural member shouldbe obtained first. For steel columns, it is relatively simple to calculate the steel temperatureusing the equations in Chapter 4, provided one has appropriate values of thermal proper-ties of the fire protection materials. For reinforced concrete columns, EN 1992-1-2contains a number of design graphs to give temperature distributions in a range of rectan-gular cross-sections at different standard fire exposure times (e.g. Fig. 4.8 of this book).For composite members and more general cases of reinforced concrete members,because the temperature distribution in the cross-section of a member is not uniform,no simple calculation procedure is available and it is necessary to employ numericalprocedures, such as the finite-element, or the finite-difference method to evaluate thenon-uniform temperature distribution. EN 1994-1-2 has provided some general heattransfer equations; however, detailed numerical implementation of these equations isbeyond the scope of this book. It is assumed that the reader has access to such a tool.To summarize, this handbook will assume that the temperature distribution in a structuralmember is available as input.

The various Eurocodes contain a number of methods to evaluate the load-carryingcapacity of different types of compressive members. For steel members, EN 1993-1-2includes the simplified calculation method and the critical temperature method. For compo-site and reinforced concrete members, EN 1994-1-2 and EN 1992-1-2 include the tabulatedmethod, the simplified calculation method and the advanced calculation method.

The tabulated method contains a number of design tables to directly relate various columndesign parameters to the available column standard fire resistance rating. These tables aregenerally based on standard fire resistance tests or results of numerical calculations andshould be used wherever possible because of their simplicity. This handbook will notrepeat these tables.

The advanced method is based on general structural engineering principles and willinevitably involve using numerical analysis procedures. This subject is beyond the scope ofthis handbook. Therefore, this handbook will mainly discuss implementations of thevarious simple calculation methods.


8.2. Effective length of columns in fireThe effective length of a column is a key parameter when calculating its compression resis-tance. The column effective length for fire limit stage design may be different from that atambient temperature.

This comes about when a column is exposed to fire attack but the column is containedwithin a fire-resistant compartment, the column rotational stiffness is reducing at elevatedtemperatures but the rotational stiffness of the cold adjacent structure is unchanged. Inrelative terms, the column is provided with increasing rotational restraint. The variousEurocodes recognize this fact and recommend using reduced column effective lengths infire compared to that at ambient temperature. Furthermore, Eurocodes assume that therelative stiffness of the adjacent cold structure to the heated column approaches infinite sothat the heated column may be considered to be rotationally fixed at the ends. Figure 8.1illustrates the Eurocode recommendations. To apply the Eurocode design recommenda-tions as illustrated in Fig. 8.1, it should be pointed out that only the adjacent coldcolumns continuous out of the fire-resistant compartment floors from the heated columnwould provide the heated column with reliable enhanced rotational restraint. This comesabout because the adjacent horizontal members would be exposed to the same fire attackas the heated column and may not provide the heated column with reliable rotationalrestraint.

(a) (b) (c)

Rigid core

Llθ

lθl

L

L

L

Fire-exposedcolumn

Fig. 8.1. Effective length of column in braced frame in fire: (a) section through building; (b) deformationmode at room temperature; and (c) deformation mode at elevated temperature

8.3. Axially loaded steel columnsBecause it is necessary to consider stability in column design, the critical temperature methodin clause 4.2.4 of EN 1993-1-2 should not be applied. The simplified calculation method forsteel columns should follow clauses 4.2.3.2 and 4.2.3.6 of EN 1993-1-2. In this method, thecolumn temperature is the starting-point of the design calculations. At the design columntemperature, the reduced column strength is calculated and compared to the applied loadin the column in fire. The column is considered to be safe if the residual column strengthexceeds the applied column load in fire. In the simplified calculation method, the appliedload in the column is assumed to remain constant during fire exposure. If the design objectiveis to find the required column fire protection thickness, an iterative procedure will benecessary. Figure 8.2 illustrates this iterative process.

The design method in EN 1993-1-2 is similar to that in EN 1993-1-1 for steel columns atambient temperature. Nevertheless, there are a number of differences. Apart from thedifference in column effective length as described in section 8.2 of this chapter, other differ-ences are concerned with column cross-section classification for local buckling and thecolumn global buckling curve. For column cross-section classification for local buckling,

64



this should be performed for fire design using a reduced value for " as given by:

" ¼ 0:85

ffiffiffiffiffiffiffiffi235

fy

sð8:1Þ

The coefficient 0.85 is an approximate value forffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikE;�=ky;�

pwhere kE;� and ky;� are the reduc-

tion factors for modulus of elasticity and effective yield strength of steel at temperature �(Table 6.1).

Using the plate width to thickness ratio limits in EN 1993-1-1 for the flanges and theweb of rolled sections under compression, it is easy to verify that all Corus-produced UC(universal column) cross-sections are class 3 or better if the steel grade is S275. If the steelgrade is S355, only sections 356� 368� 129UC and 152� 152� 23UC are class 4 cross-sections.

8.3.1. Uniformly heated column with class 1, 2 or 3 cross-sectionFor columns with class 1, 2 or 3 cross-section, there is no need to consider local buckling inthe design calculations and the column design compressive resistance Nb;fi;t;Rd is determinedfrom:

Nb;fi;t;Rd ¼ �fiAky;� fy=�M;fi ð8:2Þ

where A is the column gross cross-section area and �M;fi is the material partial safety factorfor steel at the fire limit state. �fi is the column strength reduction factor which is a functionof the column slenderness �fi and is determined from:

�fi ¼1

’� þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi’2� � �

2�

q with ’� ¼ 12½1þ �� þ �

2�� and � ¼ 0:65

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi235=fy

pð8:3Þ

When calculating the column slenderness ��, in addition to taking into consideration thereduced column effective length as described in section 8.2, it is also necessary to include theeffect of different changes in the effective yield strength and modulus of elasticity of steel at

Design satisfactory

??

Structural typeand size

Fire exposure condition

Temperature in structure

Guess fireprotectionthickness

Change

Chapter 3

Chapter 4

Reduced structuralload-carrying capacity, R

Applied load infire, E (Chapter 6)

YES NoR ≥ E?

Fig. 8.2. Design flow chart using EN 1993-1-2

65

CHAPTER 8. DESIGN OF COMPRESSION MEMBERS


elevated temperatures. EN 1993-1-2 gives the column slenderness �� as:

�� ¼ �

ffiffiffiffiffiffiffiffiky;�

kE;�

sð8:4Þ

where � is the column slenderness at ambient temperature, but calculated using the reducedcolumn effective length in fire as described in section 8.2.

If the aim of design calculations is to find the limiting temperature of the column,the column temperature is unknown and the second term on the right-hand side ofequation (8.4) cannot be calculated. However, within the practical range of steel tem-peratures (300–8008C), the second term on the right-hand side of equation (8.4) has avalue of about 1.2. Therefore, the column slenderness in fire may approximately be calcu-lated using:

�� ¼ 1:2� ð8:5Þ


Example 8.1: Calculation of the limiting temperature for a steel columnIt is required to calculate the limiting temperature of a steel column.

Input parameters

Column section size: 305� 305� 118UCHeight: 4.2m between two fire-resistant floors with the column

continuous at both endsSteel grade: S275

Applied compression loads

Permanent load: 1000 kNVariable load: 1200 kN

Calculation proceduresStep 1: Column slenderness for the fire limit stateThe column effective length at fire limit is Le;fi ¼ 0:5� 4:2 ¼ 2:1m, giving the Eulerbuckling load as:

Ncr ¼�2EI

L2e;fi

¼ �2 � 205� 90 590

2:12

�1000 ¼ 41 562 kN

The column plastic resistance at ambient temperature is:

Nu ¼ fyA ¼ 0:275� 15 000 ¼ 4125 kN

The column slenderness at ambient temperature is:

� ¼ffiffiffiffiffiffiffiNu

Ncr

s¼ 0:315

The approximate column slenderness for fire design is:

�� ¼ 1:2� � ¼ 0:378

Step 2: Column limiting temperatureAssuming a partial safety factor of 0.5 for the variable load (Table 5.1), the applied load incolumn at the fire limit state is 1000þ 1200� 0:5 ¼ 1600 kN.

66



8.3.2. Uniformly heated column with class 4 cross-sectionFor columns with class 4 cross-section where local buckling is important, EN 1993-1-2presents two alternative methods of assessing the column fire resistance. In the simplerapproach, EN 1993-1-2 recommends a conservative column limiting temperature of3508C. The alternative approach is presented in Annex E of EN 1993-1-2. In this approach,the effective width is used to consider the effects of local buckling and EN 1993-1-2 recom-mends using the identical effective widths as at ambient temperature. Afterwards, the designcalculations should proceed in the same way as for columns with class 1, 2 or 3 cross-section,except that the gross cross-sectional properties of a class 1, 2 or 3 cross-section should bereplaced by the effective cross-sectional properties of a class 4 cross-section.

8.3.3. Uniformly heated column with combined axial load and bendingmomentFor uniformly heated columns under the combined action of axial load and bendingmoment, EN 1993-1-2 provides two sets of equations, one for members with class 1, 2 and3 cross-sections and one for members with class 4 cross-sections. These equations areidentical to those at ambient temperature in EN 1993-1-1, but the member resistanceunder individual axial load or bending at elevated temperatures should be used.

8.3.4. Non-uniformly heated steel columnsThere are a number of practical situations where a steel column is non-uniformly heated, forexample a column forming part of a wall where fire exposure is from one side. At present, theEN 1993-1-2 recommendation on this issue is rather simplistic, stating that ‘the design resis-tance of a compression member with a non-uniform temperature distribution may be takenas equal to the design resistance of a compression member with a uniform temperature �equal to the maximum steel temperature’. For columns with a class 1, 2 or 3 cross-section,the EN 1993-1-2 recommendation is reasonable if the column slenderness is either verylow or very high. For columns with medium slenderness (40 < � < 100Þ, the EN 1993-1-2recommendation may not be safe. It may be necessary to employ more advanced calculationmethods. For columns with a class 4 cross-section, Annex E of EN 1993-1-2 may be used, butthe effect of thermal bowing induced bending moment should be included.

8.4. Axially loaded composite columnEN 1994-1-2 provides two alternative simplified calculation methods for composite columns.The main text (clause 4.3.5) of the code gives the general design method for all types ofcomposite columns, with specific limits of application for steel sections with partial concreteencasement (clause 4.3.5.2) and concrete-filled hollow sections (clause 4.3.5.3). Two annexesgive alternative specific calculation methods for partially encased steel sections (Annex G)and concrete-filled hollow steel sections (Annex H). This guide will describe the design

Equation (8.3) gives: � ¼ 0:601, � ¼ 0:685, �fi ¼ 0:796. Assuming a partial safetyfactor of 1.0 for steel in fire, equation (8.2) gives:

ky;� ¼ Nb;fi;t;Rd=ð�fiAfy=�M;fiÞ ¼ 1600=ð0:796� 4125=1:0Þ ¼ 0:487

From Table 6.1, the column limiting temperature is 5958C.At this temperature, the reduction factor for the modulus of elasticity of steel is 0.3245,

giving the value of the second term on the right-hand side of equation (8.4) as 1.225.According to equation (8.3), the column slenderness in fire is 0.386. This slenderness is dif-ferent from the assumed value of 0.378 and iteration is necessary.

The next iteration gives a revised column limiting temperature of 5948C, which is closeenough to the previous value and may be taken as the final column limiting temperature.

67



procedure using the general design method and provide some design aids for implementationof the alternative calculation methods of the two annexes.

8.4.1. General design methodThe general design method involves the following steps.

1. Temperatures in the composite columnSince the thermal conductivity of concrete is low, the temperature distribution in a compositecross-section is highly non-uniform. No simplified calculation method is available for heattransfer analysis of this type of column and numerical heat transfer analysis softwareshould be used to perform this task.

2. Cross-sectional properties at elevated temperaturesTwo values of the composite cross-section should be calculated: the cross-section plasticresistance to axial compression and the cross-section effective flexural stiffness. When per-forming these calculations, the composite cross-section is divided into a large number ofblocks each having approximately the same temperature. The property of the compositecross-section is obtained by summing up contributions of all the blocks. Use the subscriptsa, s and c to represent the steel profile, reinforcing bars and concrete respectively.

The plastic resistance to axial compression of the composite cross-section is:

Nfi;pl;Rd ¼Xj

ðAa;� fay;�Þ=�M;fi;a þXk

ðAs;� fsy;�Þ=�M;fi;s þXm

ðAc;� fc;�Þ=�M;fi;c ð8:6Þ

where the composite cross-section is divided into j-blocks of steel, k reinforcing bars and m-blocks of concrete. For each block of the composite cross-section, A is its area and f thedesign strength of its material at the appropriate temperature. The �-factors are materialpartial safety factors for fire design.

Similarly, the effective flexural stiffness of the composite cross-section is:

ðEIÞfi;eff ¼Xj

ð’a;�Ea;�Ia;�Þ þXk

ð’s;�Es;�Is;�Þ þXm

ð’c;�Ec;sec;�Ic;�Þ ð8:7Þ

where E is the initial modulus of elasticity of steel or reinforcement at temperature �. Forconcrete, the secant modulus should be used, this being calculated as the design compressionstrength of concrete ( fc;�Þ divided by the corresponding strain at peak stress "c1;�, whosevalues are given in Table 6.4. For each block of the composite cross-section, I is itssecond moment of area around the relevant axis of the entire cross-section.

Equation (8.7) contains a set of reduction coefficients (’Þ, which have been introduced toaccount for the effect of thermal stresses caused by non-uniform temperature distribution inthe composite cross-section and unequal thermal expansions in different materials. In prin-ciple, this non-uniform thermal strain distribution gives rise to non-uniform mechanicalstrain distribution in the composite cross-section. Since the stress–strain relationships ofsteel and concrete are non-linear, this non-uniform distribution of mechanical strainswould result in a different distribution of material stiffness around the composite cross-section from that based on uniform strain distribution. The general calculation method inclause 4.3.5.1(5) of EN 1994-1-2 does not give values to these reduction coefficients. InAnnex G for partially encased steel sections, different values are given for different standardfire resistance ratings. These values may be used in the general calculation method for designunder the standard fire exposure. Since the general calculation method is not limited to thestandard fire exposure and may be applied to other types of fire exposure, e.g. parametricfire curves in EN 1991-1-2 (Chapter 3 of this guide), it is recommended that the designershould use the lower values in Annex G so as to be on the safe side. For concrete-filledsteel hollow sections, Annex H does not include these reduction coefficients, implying thatthey have a value of unity. This should be adopted when using the general calculationmethod, irrespective of the type of fire exposure.

68



3. Column resistance to axial compressionUsing the effective flexural stiffness of the composite cross-section, the Euler buckling load ofthe composite column is calculated by:

Nfi;cr ¼ �2ðEIÞfi;eff

L2�

ð8:8Þ

where the effective length of the composite column in fire Le;� should be evaluated followingSection 8.2.

The non-dimensional slenderness ratio of the composite column in fire is:

�� ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiNfi;pl;R

Nfi;cr

sð8:9Þ

in which Nfi;pl;R is the value of Nfi;pl;Rd according to equation (8.6), but with the materialpartial safety factors set to unity.

The resistance of the composite column to axial compression is obtained from:

Nfi;Rd ¼ �Nfi;pl;Rd ð8:10Þ

in which the buckling curve ‘c’ of EN 1993-1-1 should be used to obtain the reduction coeffi-cient � irrespective of the type of composite cross-section.

When using the general calculation method, the limits of applicability in clause 4.3.5.2(2)for partially encased steel sections and in clause 4.3.5.3(2) for concrete-filled hollow sectionsshould be observed.

The general design method is only applicable to axially loaded composite columns. Forcomposite columns with eccentricity, the alternative design methods in Annex G andAnnex H should be followed.

Example 8.2: General design methodInput informationThe cross-section for this example is a concrete-filled circular hollow section (CHS)355.6� 12.5mm. The material properties are as follows:

Structural steel: fy ¼ 275N/mm2, Ea ¼ 210 kN=mm2, �ma ¼ 1:0Concrete: fck ¼ 25N/mm2, Ecm ¼ 30:5 kN/mm2, �ma ¼ 1:1

The column is 4.5m high and is bounded by fire-resistant floors and continuous at bothends.

This example will determine the compressive strength of the column at standard fire-resistance rating R60, with no external fire protection and no internal reinforcement.

Results of calculationStep 1: Temperature distribution in the composite cross-sectionFor simplicity, the approximate method of Lawson and Newman40 is used. In thisexample, the steel shell is treated as one layer of uniform temperature and the concretecore is divided into ten layers. To account for the steep temperature gradient at theouter layers of the concrete core, each of the five outer layers of the concrete core willhave a thickness of 10mm. The remaining inner concrete core is divided into fivelayers, each having a thickness of 23.06mm.

Assuming an ambient temperature of 208C, the approximate method of Lawson andNewman40 gives temperatures for each layer of the composite cross-section in Table 8.1.

Step 2: Composite cross-section propertiesAt the elevated temperatures in Table 8.1, the reduced effective yield strength andmodulus of elasticity of steel, the reduced design strength and secant modulus of concretecan be obtained from Tables 6.1 and 6.4 respectively. These values are also listed inTable 8.1.

69



Table 8.1. Results of calculation for worked Example 8.2

LayerInner–outerradius (mm) � (8C) ky;� "cu � 1000

f�(N/mm2)

E�(N/mm2)

Steel 165.3–177.8 827.1 0.066 N/A 18.15 8589L1 155.3–165.3 518 0.573 10.04 14.33 1427L2 145.3–155.3 432 0.702 8.14 17.55 2156L3 135.3–145.3 353 0.797 6.795 19.93 2933L4 125.3–135.3 281 0.8595 5.715 21.49 3760L5 115.3–125.3 203 0.8985 4.545 22.46 4962L6 92.24–115.3 188 0.906 4.38 22.65 5171L7 69.18–92.24 132 0.934 3.82 23.35 6113L8 46.12–69.18 125 0.9375 3.75 23.44 6251L9 23.06–46.12 125 0.9375 3.75 23.44 6251L10 0–23.06 125 0.9375 3.75 23.44 6251

For each layer, its area (AÞ and the second moment of area (IÞ can be calculated usingthe following equations:

A ¼ �2

4ðD2

o �D2i Þ ð8:11aÞ

I ¼ �2

64ðD4

o �D4i Þ ð8:11bÞ

where Do and Di are the outer and inner diameter of the layer respectively.Using equations (8.6) and (8.7) and results in Table 8.1, the plastic resistance and effec-

tive flexural stiffness of the composite column are:

Nfi;pl;Rd ¼ 1605 kN

Nfi;pl;R ¼ 1741 kN

ðEIÞfi;eff ¼ 3682 kN:m2

Step 3: Column compression resistanceAccording to Section 8.2, the column effective length at the fire limit state is:

Le; fi ¼ 0:5� 4:5 ¼ 2:25m

The Euler buckling load is:

Nfi;cr ¼�2 � 3682

2:252¼ 7178 kN

giving the column slenderness as:

�� ¼ffiffiffiffiffiffiffiffiffiffi1741

7178

r¼ 0:492

Using buckling curve ‘c’ of EN 1993-1-1, the column strength reduction factor is� ¼ 0:8473, giving the compression resistance of the column as:

Nfi;Rd ¼ 0:8473� 1605 ¼ 1360 kN

For comparison, according to EN 1994-1-1, the compression resistance of the columnat ambient temperature may be calculated to be 4336.7 kN. Therefore, at the standardfire resistance rating of R60, the unprotected and unreinforced composite column has aresidual strength of 31.4% of its resistance at ambient temperature.

70



8.4.2. Alternative design method for composite column with partiallyencased steel sectionThe alternative design method follows the general calculation method, presented in theprevious section. It should be pointed out that the alternative design method is only applicableto bending about the weak axis of the cross-section. Also the limits of application of the alter-native designmethod (clause G.6(5)) are different from those of the general calculation method(clause 4.3.5.2(2)). This alternative method is applicable only to the standard fire exposure.

The alternative design method differs from the general calculation method in calculationsof the properties of the composite cross-section. In the general calculation method, thecomposite cross-section is divided into numerous small blocks. In the alternative method,the composite cross-section is divided into only four large components: the flanges of thesteel profile, the web of the steel profile, the concrete contained by the steel profile and thereinforcing bars.

The flanges of the steel profile are assumed to have the same temperature and Annex G.2gives information on how to calculate this temperature value for different standard fireresistance ratings.

The web of the steel profile is assumed to have a reduced height with the same modulus ofelasticity as at ambient temperature, but a reduced strength.

For concrete, it is also assumed to be at uniform temperature but with reduced dimensions.For the reinforcing bars, the reduction factors for their effective yield strength and

modulus of elasticity are directly given depending on the design standard fire resistancerating and the concrete cover.

The following paragraphs will present design aids to assist in implementing the alternativedesign method in Annex G.

8.4.2.1. Design aids for the web of the steel profile (Annex G.3)Figure 8.3 shows the various symbols used in the calculations. The part of the web withheight hw;fi, measured from the inner edge of the flange, should be neglected. The calculationsin Annex G.3 involves using the factor ½

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� 0:16ðHt=hÞ

p�, where Ht is an empirical number

depending on the design standard fire resistance rating and h is the depth of the steel sectionas shown in Fig. 8.3. Denoting this factor by �, Fig. 8.4 plots the �-value as a function of thesteel section depth for different standard fire resistance ratings.

Using this value, the effective depth of the web is:

dw;fi ¼ h� 2ef � 2hw;fi ¼ ðh� 2efÞ�1� 2

hw;fih� 2ef

�

¼ ðh� 2efÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� ð0:16Ht=hÞ

p¼ �ðh� 2efÞ ð8:12Þ

The maximum stress level is obtained from:

fay;w;t ¼ fay;wffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� ð0:16Ht=hÞ

p¼ �fay;w ð8:13Þ

Y

Z

h

b

bc,fihw,fi

ef

ewu2

u1

bc,fi

Fig. 8.3. Reduced cross-section for partially encased steel sections

71



Rearranging the equations in Annex G.3, the following equations may be used to calculatethe contributions of the web of the steel profile to the plastic resistance and effective flexuralstiffness of the composite cross-section:

Nfi;pl;Rd;w ¼ ewdw;fi fay;w;t=�M;fi;a ð8:14Þ

ðEIÞfi;w;z ¼ Ea;wdw;fie3w=12 ð8:15Þ

Example 8.3: Alternative design method for composite column with thepartially encased steel sectionCalculate the plastic resistance and flexural rigidity of a partially encased steel section witha 305� 305� 137UC profile for a standard fire resistance rating R60. The steel is gradeS355 and the design concrete strength at ambient temperature is 40N/mm2. Assume silic-eous aggregates. The material partial safety factors are 1.0. When calculating the effectiveflexural rigidity ðEIÞfi;eff;z, use values of �f;� ¼ 0:9, �w;� ¼ 1:0 and �s;� ¼ 0:8 for the flanges,the web and concrete respectively according to Table G.7 of EN 1994-1-2.

Results of calculationThe dimensions of the cross-section are: overall width b ¼ 309:2mm, overall depthh ¼ 320:5mm, flange width b ¼ 309:2mm, flange thickness ef ¼ 21:7mm, webdepth¼ 277.1mm, web thickness ew ¼ 13:8mm.

Section factor Am=V ¼ 2� ð0:3092þ 0:3205Þ=ð0:3092� 0:3205Þ ¼ 12:71m�1

FlangesFrom clause G.2(1) and Table G.1, the steel flange temperature is:

�f;t ¼ 680þ 9:55� 12:71 ¼ 801:48C

From Table 6.1, the maximum stress level is 0:1093� 355 ¼ 38:80N/mm2. The elasticmodulus is 0:0897� 205 000 ¼ 18 388:5N/mm2.The plastic resistance of the flanges is:

Nfi;pl;Rd;f ¼ 2� 309:2� 21:7� 38:8=1000 ¼ 520:7 kN

The effective flexural rigidity of the flanges is:

ðEIÞfi;f;z ¼ 18 388:5� 21:7� 309:23=6=109 ¼ 1966 kN:m2

0.1

0

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 100 200 300 400 500 600 700 800 900 1000

Section depth h (mm)

β

R30R60R90R120

Fig. 8.4. Value of � ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� 0:16ðHt=hÞ

pas a function of depth of composite cross-section

72



8.4.2.2. Some design tablesAlthough the detailed design calculation equations in Annex G are clearly presented andshould be easy to follow, as demonstrated by the worked Example 8.3, they still require alarge amount of calculation effort. To help designers make use of this type of compositecolumn, calculations have already been performed to obtain the contributions of the differ-ent components of a partially encased composite cross-section to its plastic resistance andeffective flexural stiffness for the Corus-manufactured UC steel sections.

Tables 8.2 to 8.5 present these calculation results, giving the plastic resistance and effectiveflexural stiffness of the flanges of the steel profile, the web of the steel profile and concrete.The tables have been generated using the following material properties:

Steel: fy ¼ 275N/mm2, E ¼ 205 000N/mm2, �M;fi;a ¼ 1:0

Concrete: fc ¼ 25N/mm2, Ec;sec ¼ 25=0:0025 ¼ 10 000N/mm2, �M;fi;c ¼ 1:0

For completeness, Tables 8.2–8.5 give values for all Corus UC sections for fire resistancerating up to R120. However, it is clear that it would not be appropriate to use some of thesmaller sections for high fire resistance rating.

These tables do not include reinforcing bars because they do not have fixed sizes or posi-tions, and calculating their contributions is relatively simple and straightforward.

If the material properties or the partial safety factors are different from above, the valuesin Tables 8.2–8.5 should be modified by the ratios of the appropriate new design property tothe assumed value.

WebTable G.2 gives Ht ¼ 770mm.

� ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� ð0:16Ht=hÞ

p¼ 0:7846

From equation (8.12), the effective depth of the web is:

dw;fi ¼ 0:7846� 277:1 ¼ 217:4mm

From equation (8.13), fay;w;t ¼ 0:7846� 355 ¼ 278:53N/mm2.From equations (8.14) and (8.15):

Nfi;pl;Rd;w ¼ 13:8� 217:4� 278:53=1000 ¼ 835:6 kN

ðEIÞfi;w;z ¼ 205 000� 217:4� 13:83=12=109 ¼ 9:8 kN:m2

ConcreteAccording to Table G.3, bc;fi ¼ 15:0mm.

From Table G.4, �c;t ¼ 330:98C. From Table 6.4, kc;� ¼ 0:819, "cu;� ¼ 0:007927.

Ec;sec;� ¼ 40� 0:819=0:007927 ¼ 4133:12N=mm2

fc;� ¼ 0:819� 40 ¼ 32:76N=mm2

From Clause G.4(4):

Nfi;pl;Rd;c ¼ 0:86� ð320:5� 2� 21:7� 2� 15Þ � ð309:2� 13:8� 2� 15Þ � 32:76=1000

¼ 1847:85 kN

ðEIÞfi;c;z ¼ 4133:2� ð320:5� 2� 21:7� 2� 15Þ � ½ð309:2� 2� 15Þ3 � 13:83�=12=109

¼ 1852:1 kN:m2

The total plastic resistance is:

Nfi;pl;Rd ¼ 520:7þ 835:6þ 1847:85 ¼ 3204:2 kN

The total effective flexural rigidity is:

ðEIÞfi;eff;z ¼ 0:9� 1966þ 1:0� 9:8þ 0:8� 1852:1 ¼ 3260:88 kN:m2

73



Table 8.2. Plastic resistance and effective flexural stiffness of different parts of partially encased steelsection, standard fire resistance R30

Flanges Web Concrete

UC profile

Plasticresistance(kN)

Effectiveflexuralstiffness(kN.m2Þ





356� 406� 634

356� 406� 551

356� 406� 467

356� 406� 393

356� 406� 340

356� 406� 287

356� 406� 235

356� 368� 202

356� 368� 177

356� 368� 153

356� 368� 129

305� 305� 283

305� 305� 240

305� 305� 198

305� 305� 158

305� 305� 137

305� 305� 118

305� 305� 97

254� 254� 167

254� 254� 132

254� 254� 107

254� 254� 89

254� 254� 73

203� 203� 86

203� 203� 71

203� 203� 60

203� 203� 52

203� 203� 46

152� 152� 37

152� 152� 30

152� 152� 23

6880

5867

4885

4027

3433

2853

2302

1907

1658

1422

1185

2496

2067

1664

1282

1091

923

744

1180

891

693

564

453

460

374

301

259

225

114

88

62

49105

40695

32775

26263

21903

17798

14021

10412

8935

7563

6230

9932

7997

6252

4689

3929

3276

2596

3007

2179

1645

1304

1035

758

607

489

418

362

133

104

73

555

383

235

146

96

59

32

23

15

9

6

84

53

30

17

11

7

4

25

12

7

4

2

5

3

2

1

1

1

1

0

3701

3256

2751

2337

2022

1709

1384

1237

1076

917

773

1729

1474

1216

998

868

752

617

961

757

628

502

416

473

369

343

287

260

200

160

140

2255

2252

2250

2247

2245

2242

2240

2126

2125

2123

2122

1495

1493

1491

1488

1487

1486

1485

988

986

984

983

982

610

609

608

607

606

327

326

325

8233

7859

7447

7112

6861

6615

6364

5366

5256

5148

5049

2822

2701

2580

2477

2417

2364

2303

1161

1096

1055

1016

989

397

377

371

361

355

98

94

92

74





UC profile







356� 406� 634

356� 406� 551

356� 406� 467

356� 406� 393

356� 406� 340

356� 406� 287

356� 406� 235

356� 368� 202

356� 368� 177

356� 368� 153

356� 368� 129

305� 305� 283

305� 305� 240

305� 305� 198

305� 305� 158

305� 305� 137

305� 305� 118

305� 305� 97

254� 254� 167

254� 254� 132

254� 254� 107

254� 254� 89

254� 254� 73

203� 203� 86

203� 203� 71

203� 203� 60

203� 203� 52

203� 203� 46

152� 152� 37

152� 152� 30

152� 152� 23

2723

2314

1918

1575

1338

1108

890

733

635

543

452

939

772

618

472

403

343

279

467

360

284

234

189

192

156

125

108

94

54

43

31

20832

17407

14152

11446

9617

7877

6260

4718

4069

3463

2868

4706

3839

3045

2319

1966

1658

1332

1736

1311

1023

833

666

494

396

320

274

237

91

71

50

508

349

213

132

86

52

28

20

13

8

5

74

46

26

15

10

6

4

21

10

6

3

2

4

2

2

1

1

1

0

0

3107

2708

2266

1905

1634

1369

1098

976

845

715

599

1353

1140

928

751

647

556

453

684

526

427

337

275

282

214

193

158

141

73

54

42

1841

1837

1832

1827

1824

1820

1816

1714

1712

1710

1708

1167

1164

1160

1157

1155

1153

1151

731

728

725

723

722

417

415

414

413

412

192

191

189

4503

4272

4021

3817

3665

3516

3364

2794

2728

2664

2606

1385

1316

1249

1191

1158

1128

1094

510

477

455

436

422

148

140

137

132

130

27

25

24

75





UC profile







356� 406� 634

356� 406� 551

356� 406� 467

356� 406� 393

356� 406� 340

356� 406� 287

356� 406� 235

356� 368� 202

356� 368� 177

356� 368� 153

356� 368� 129

305� 305� 283

305� 305� 240

305� 305� 198

305� 305� 158

305� 305� 137

305� 305� 118

305� 305� 97

254� 254� 167

254� 254� 132

254� 254� 107

254� 254� 89

254� 254� 73

203� 203� 86

203� 203� 71

203� 203� 60

203� 203� 52

203� 203� 46

152� 152� 37

152� 152� 30

152� 152� 23

1437

1232

1032

856

733

612

497

415

362

312

261

559

467

379

295

252

215

174

291

224

177

146

119

132

109

89

77

68

47

37

27

15344

12879

10523

8553

7214

5934

4737

3596

3110

2653

2203

3664

3007

2401

1841

1562

1319

1060

1391

1053

823

671

537

405

326

263

225

196

78

61

43

469

320

194

120

78

47

25

18

12

7

4

66

41

23

13

8

5

3

17

8

5

2

1

3

1

1

1

0

0

0

0

2640

2278

1884

1565

1330

1102

873

771

663

557

463

1058

878

702

556

474

403

323

466

345

270

207

164

132

92

75

58

48

0

0

0

1494

1485

1476

1466

1459

1452

1444

1350

1345

1341

1337

870

863

856

849

846

842

838

485

479

474

470

466

224

221

218

216

215

63

62

60

2750

2581

2399

2250

2140

2034

1926

1558

1513

1469

1428

700

656

613

576

555

537

516

205

186

174

164

156

39

36

35

33

32

3

2

2

76





UC profile







356� 406� 634

356� 406� 551

356� 406� 467

356� 406� 393

356� 406� 340

356� 406� 287

356� 406� 235

356� 368� 202

356� 368� 177

356� 368� 153

356� 368� 129

305� 305� 283

305� 305� 240

305� 305� 198

305� 305� 158

305� 305� 137

305� 305� 118

305� 305� 97

254� 254� 167

254� 254� 132

254� 254� 107

254� 254� 89

254� 254� 73

203� 203� 86

203� 203� 71

203� 203� 60

203� 203� 52

203� 203� 46

152� 152� 37

152� 152� 30

152� 152� 23

928

800

674

562

483

405

331

279

244

210

176

384

323

264

207

178

152

124

215

168

134

111

90

101

83

68

59

51

36

28

20

11662

9789

7999

6501

5484

4511

3601

2734

2364

2017

1675

2786

2286

1825

1400

1188

1003

806

1058

801

626

510

409

308

248

200

172

149

59

47

33

449

306

185

113

73

44

24

17

11

7

4

61

38

21

12

8

5

3

15

7

4

2

1

2

1

1

0

0

0

0

0

2428

2082

1710

1410

1191

980

771

678

580

485

401

924

758

599

468

395

333

264

367

262

199

148

114

63

36

21

12

6

0

0

0

1120

1104

1087

1071

1058

1045

1031

944

937

930

922

545

534

523

512

505

499

493

229

219

212

207

202

51

48

46

44

43

0

0

1

1465

1346

1222

1121

1048

977

907

699

671

644

619

259

236

213

194

183

174

164

46

39

35

32

29

2

2

2

1

1

0

0

0

77



An example is given below to illustrate how to use these tables.

Eccentricity of loadingIn buildings, columns may be subjected to some eccentricity of loading. Calculating the com-pressive resistance of composite columns under eccentricity is already a rather complicatedand long process at ambient temperature. Adding non-uniform temperature distribution tothese calculations makes it extremely difficult to derive a simple hand-calculation method.However, for composite columns with nominal eccentricity, since the effect of eccentricityis relatively small, Annex G of EN 1994-1-2 allows the following simple scaling equationto be used to calculate the reduced column compressive resistance under eccentricity ofloading in fire:

Nfi;Rd; ¼ Nfi;Rd

NRd;

NRd

ð8:16Þ

where NRd and NRd; are the compressive resistance of the column at ambient temperaturewith and without eccentricity of loading respectively. Nfi;Rd is the compressive resistanceof the column without eccentricity of loading in fire.

8.4.3. Alternative design method for composite columns with concrete-filledhollow sectionsThe alternative design method in Annex H of EN 1994-1-2 is completely different from thegeneral design method presented in Section 8.4.1.

When using the alternative design method in Annex H, a step-by-step approach should betaken, with the strain of the column increasing until the design compressive resistance toaxial loading is obtained. At each step, the plastic resistance and Euler buckling load ofthe composite column are evaluated. The plastic resistance of the column is calculated differ-ently from that in the general calculation method. It is calculated as the sum of the area ofeach component of the column cross-section times its stress. Here the stress is taken from thestress–strain relationship of the material at the column strain of the current step. Therefore,

Example 8.4: Use of design tablesUsing the information in Table 8.3, recalculate the plastic resistance and effective flexuralstiffness of the section in worked Example 8.3.

Results of calculationFrom Table 8.3, the contributions of the flanges of the steel profile, the web of the steelprofile and concrete to the plastic resistance and effective flexural stiffness of the compo-site cross-section are:

Nfi;pl;Rd (kN) ðEIÞfi;eff;z (kN.m2Þ

Flanges 403.4 1955.9Web 647.4 9.8Concrete 1154.9 1157.6

The plastic resistance of the composite cross-section is:

Nfi;pl;Rd ¼ ð403:4þ 647:4Þ � 355=275þ 1154:9� 40=25 ¼ 3204:3 kN

The effective flexural rigidity of the composite cross-section is:

ðEIÞfi;eff;z ¼ 0:9� 1955:9þ 9:8þ 0:8� 40=25� 1157:6 ¼ 3260:93 kN:m2

78



as the strain of the material increases, the plastic resistance of the composite column alsoincreases. This is illustrated as curve 1 in Fig. 8.5. In the meantime, the Euler bucklingload of the composite column is calculated using the tangent modulus of the stress–strainrelationship of the material at the material temperature and strain of the current step. Asthe tangent modulus of the material decreases at increasing strain, the Euler buckling loadof the composite column also decreases with increasing strain. This is shown as curve 2 inFig. 8.5. When these two curves meet, the plastic resistance of the column becomes equalto the Euler load of the column and this value is the design compressive strength of thecomposite column.

Annex H has not specified any limit of application of the alternative design method. To beon the safe side, the limits of application of the general design method in clause 4.3.5.3(2) ofEN 1994-1-2 should be observed.

The alternative design method in Annex H of EN 1994-1-2 will be extremely difficult toperform by hand. Not only does it involve dealing with non-uniform temperature distribu-tions, but it also requires using detailed stress–strain relationships of the concrete and steel atelevated temperatures. Designers are encouraged to use the general design method.

8.4.3.1. Eccentricity of loadingSimilar to the alternative design method for composite columns with partially encased steelsections, the eccentricity of loading is also treated in a simplistic way. For concrete-filledtubular columns, the design strength of the composite column with eccentricity of loadingis obtained by multiplying the design strength of the axially loaded composite column bytwo factors, one depending on the percentage of reinforcement (�sÞ and one on thecolumn slenderness and eccentricity of loading (�Þ. The values of these modificationfactors are presented in graphic form as Figs H1 and H2 of EN 1994-1-2 respectively.

8.5. Reinforced concrete columnsEN 1992-1-2 provides two simplified calculation methods for reinforced concrete columns,the ‘5008C isotherm method’ in Annex B.1 and the ‘zone method’ in Annex B.2. Forreinforced concrete columns exposed to the standard fire condition, either method may beused. For reinforced concrete columns under parametric fire curves of EN 1991-1-2

Curve 1: plasticresistance

Curve 2: Eulerbuckling ld

Load

Strain

Designresistance

Fig. 8.5. Design resistance of columns with concrete-filled hollow section using Annex H

79



(Chapter 3), only the 5008C isotherm method can be used. If the parametric fire curves areadopted, the opening factor of the fire compartment (Section 3.5) should not be less than0.14m1=2.

8.5.1. 50088C isotherm methodThis method assumes that concrete heated above 5008C has no strength or stiffness whileconcrete below 5008C retains the full strength and stiffness at ambient temperature. The con-crete column is then designed as at ambient temperature, but using the reduced cross-sectionsize. All reinforcing bars should be included in the calculations even if some of them may falloutside the reduced concrete cross-section. The strength of any reinforcing bar should be thatat the appropriate elevated temperature.

8.5.2. Zone methodThe zone method is only suitable for rectangular cross-sections. In this method, the originalconcrete cross-section is reduced to allow for fire damage. The damaged zone is a function ofthe temperature distribution of the entire concrete cross-section. Only the remaining concretecross-section (the original cross-section minus the damaged zone) is then used in columnstrength calculations. Unlike the 5008C isotherm method, the reduced concrete cross-section has reduced strength and modulus of elasticity.

It is best using an example to illustrate the application of this method.

Example 8.5: Application of the zone methodFigure 8.6 shows a rectangular concrete cross-section which is heated from all four sur-faces. In the zone method, it is assumed that the damaged zone has the same thicknesson both the short and long sides of the cross-section, being that determined for theshort side of the cross-section. Therefore, for the cross-section shown in Fig. 8.6(a), thewidth (short side ¼ 2w1Þ of the concrete cross-section is reduced by 2az1 and the length(long side) of the concrete cross-section is also reduced by 2az1.

w1 w1

az1

kc(θM1)

az1

az1

(a)

w1

M1

w1

az1 az1

(b)

kc(θM1)

Fig. 8.6. Determination of reduced concrete cross-section for reinforced concrete columns: (a)column cross-section; and (b) equivalent wall

To determine the damaged zone of the short side, the effect of the long side is ignored,so that the column cross-section becomes an equivalent wall (Fig. 8.6(b)). Assume that thewall thickness is 2w1 and that the centre of the wall is represented by point M1 anywherealong the centre line of the wall.The half-thickness (w1Þ of the wall is divided into n-parallel zones of equal thickness

(n � 3Þ. Each zone is assumed to have the same temperature as that at the centre of the

80



8.5.3. Additional commentsComparing the 5008C isotherm method and the zone method, it is clear that the zone methodis much more laborious. Therefore, it is recommended that the 5008C isotherm method beused wherever possible. The zone method should only be used when the column wouldnot have sufficient resistance when designed using the 5008C isotherm method and it isnot possible to increase the cross-section size or the reinforcement.

Both the 5008C isotherm and the zone methods may be used to design columns withcombined axial load and bending moments.

For a reinforced concrete column under fire condition, because of the reduction in itseffective cross-section size and reduction in the modulus of elasticity at elevated tempera-tures, the second-order effect will become more pronounced than at ambient temperature.If the concrete column becomes slender according to the definition of EN 1992-1-1,Annex B.3 of EN 1992-1-2 should be followed to deal with the increased second-ordereffect. This design method follows the ambient temperature method in EN 1992-1-1 butis rather complex and numerical implementation of this method would be necessary.Alternatively, the tabulated results in Annex C of EN 1992-1-2 may be used, which havebeen generated by numerically implementing the calculation procedure in Annex B.3.

Advanced calculation methods should be used for reinforced concrete columns ofnon-rectangular cross-section.

zone. Table 6.4 can be used to find the compressive strength reduction factor of the zone atthe zone temperature. The mean strength reduction factor of the entire half-thickness ofthe wall is calculated by:

kc;m ¼ ð1� 0:2=nÞn

Xni¼1

kcð�iÞ ð8:17Þ

where the subscript i indicates the zone number, �i its temperature and kcð�iÞ the strengthreduction factor of the zone. The factor (1� 0:2=nÞ is incorporated to allow for variationin temperature within each zone.

The thickness of the fire-damaged zone is given by:

az1 ¼ w1

�1�

�kc;m

kcð�mÞ

��ð8:18Þ

where �m is the temperature and kcð�mÞ the strength reduction factor at point M1 alongthe centre line of the wall. � ¼ 1:3 for compression members (columns and walls) and� ¼ 1 for bending members (beams and slabs).

If the column is not heated on four sides, the damaged zone should be taken out onlyfrom the sides of the cross-section that are exposed to fire. If the column is heated fromone side only, it forms half of the equivalent wall in Fig. 8.6(b). By deduction, if therectangular cross-section of a column is heated from three sides with the unheated sidebeing the shorter dimension of the cross-section, the half-thickness of the equivalentwall in Fig. 8.6(b) should be the lesser of the shorter dimension or half of the longerdimension.

Having determined the reduced concrete cross-section, the design compressive resis-tance of the reinforced concrete column is calculated using the ambient temperaturedesign method in EN 1992-1-1, but the design strength and modulus of elasticity ofconcrete should be reduced according to the temperature at point M1 along the centreline of the cross-section. As in the 5008C isotherm method, the reinforcing bars shouldbe calculated individually, including any reinforcing bar that may fall outside thereduced concrete cross-section.

81



CHAPTER 9

Design of bending members

9.1. IntroductionThis chapter will provide guidance on the design of bending members (beams), includingsteel beams, composite beams and reinforced concrete beams. For composite beams,EN 1994-1-2 gives a number of approximate calculation methods for different types ofcomposite beam. They will be dealt with separately.

It is assumed that temperatures in the cross-section of the beam are given as input data.Alternatively, readers should refer to the guidance in Chapter 4.

9.2. Steel beamsDesign calculations for steel beams at the fire limit state are similar to those in EN 1993-1-1at ambient temperature. In EN 1993-1-2, a steel beam should be checked for:

. sufficient bending moment capacity

. sufficient shear resistance

. sufficient lateral torsional buckling resistance

. deformation limit.

9.2.1. Bending moment capacitySteel beams are normally exposed to fire attack from three sides with the top of the beamsbeing insulated by the floors, therefore temperature distribution in the cross-section of abeam tends to be non-uniform. The non-uniform temperature distribution means that thesteel strength and stiffness will be different at different locations of the cross-section,which should be accounted for in design calculations.

In EN 1993-1-2, the bending moment capacity of a class 1 or 2 cross-section is equalto the plastic bending moment capacity of the cross-section, which may be calculatedusing two methods. In the first method which is called the plastic bending momentcapacity method (clause 4.2.3.3(2)), the steel cross-section is divided into a number ofblocks. Each block is assumed to reach its yield strength. After finding the plastic neutralaxis of the cross-section, which divides the cross-section into a compression part and atension part with the same axial capacity, the plastic bending moment capacity of thecross-section is obtained by summing up contributions of all the blocks. This methodrequires information about temperatures of the entire cross-section. In the alternativemethod (clause 4.2.3.3(3)), the plastic bending moment capacity of the cross-section withnon-uniform temperature distribution is related to that with uniform temperature distribu-tion as follows:

Mfi;t;Rd ¼Mfi;�;Rd

�1ð9:1Þ


where Mfi;t;Rd is the plastic bending moment capacity of the cross-section with non-uniformtemperature distribution, �1 (¼ 0.7) is a modification factor and Mfi;�;Rd is the plasticbending moment capacity of the cross-section at a uniform temperature �. Leaving out thematerial partial safety factors, Mfi;�;Rd is obtained by multiplying the plastic bendingmoment capacity of the cross-section at ambient temperature by the yield strength reductionfactor of steel (ky;� in Table 6.1). In EN 1993-1-2, the uniform temperature � is referred to as‘the uniform temperature �a at time t in a cross-section which is not thermally influenced by thesupports’. This is a rather confusing definition. Since the lower flange of the cross-section is themost critical element, the uniform temperature � should be taken as that of the lower flangeaway from the supports.

For class 3 cross-sections, equation (9.1) should be used. However,Mfi;�;Rd should be takenas the elastic bending moment capacity of the cross-section at a uniform temperature �.

An example is provided below to illustrate the two calculation methods.

Example 9.1: Calculation of benching moment capacityFigure 9.1 shows the temperature distribution in the cross-section of a steel beam made of457� 152� 67UB. It is required to evaluate the plastic bending moment of the cross-section. The steel grade is S275 and the material safety factor is 1.0.

Top flange: 550°C

Centre line: 750°C

Bottom flange: 750°C

Fig. 9.1. Assumed temperature distribution for Example 9.1

Calculation resultsMethod 1: plastic bending moment capacity methodThe cross-section may be checked to be class 1. The cross-section is divided into five layersconsisting of: the top flange (153.8mm by 15.0mm), the top-most 1

4 of the web, 14 of the

web just above the centre line (upper 14 web),

12 of the web below the centre line (lower 1

2

web) and the lower flange. The root radius area of the entire cross-section is assumedto be equally distributed along the web so that a web thickness of 9.22mm is used inthe calculations. Results are summarized in Table 9.1 where it is assumed that thelower part of the cross-section is in tension and the upper part in compression. Sincethe top flange has more compressive capacity than the combined tensile capacity of theother parts, the plastic neutral axis is in the top flange which is further divided into twolayers, one in compression (14.876mm thick) and one in tension (0.124mm thick) sothat the tensile and the compressive capacities of the cross-section are equal.

Table 9.1. Results of calculation for Example 9.1

Layer

Layertemperature(8C)

Design strength(N/mm2Þ

Capacity(kN)

Lever arm toPNA (mm)

Momentresistance(kN.m)

Top flange 550 0:625� 275 ¼ 171:9 393.3 (C)3.28 (T)

7.438 (C)0.062 (T)

2.9250.002

Top 14 web 600 0:47� 275 ¼ 129:25 127.5 (T) 53.624 (T) 6.837

Upper 14 web 700 0:23� 275 ¼ 63:25 62.40 (T) 160.624 (T) 10.023

Lower 12 web 750 0:17� 275 ¼ 46:75 92.24 (T) 321.124 (T) 29.620

Lower flange 750 46.75 107.85 (T) 435.624 (T) 46.982

Total — — C¼T¼ 393.3 — 96.389

PNA¼ plastic neutral axis

84



The critical temperature methodSometimes the aim of the beam design calculations is to find out the maximum temperaturethat the beam can sustain at a given load. If there is no problem of lateral torsional buckling(which is almost always true at the fire limit state) and the beam design is governed by thebending moment capacity, the critical temperature method in clause 4.2.4 of EN 1993-1-2may be used. The critical temperature is the maximum temperature that the beam cansustain and the critical temperature method is in fact the same method as the limitingtemperature method in BS 5950 Part 8.12 In the critical temperature method, the criticaltemperature of the beam is related to the degree of utilization (�0Þ of the beam, which isthe ratio of the applied maximum bending moment in the beam at the fire limit state tothe beam’s bending moment capacity at ambient temperature, i.e. the plastic bendingmoment capacity for a class 1 or 2 cross-section or the elastic bending moment capacityfor a class 3 cross-section. For a cross-section with non-uniform temperature distribution,the degree of utilization should be modified by multiplying it by factor �1 (¼ 0.7). Therelationship between the critical temperature method and the utilization factor is:

�a;cr ¼ 39:19 ln

�1

0:9674�3:8330

� 1

�þ 482 ð9:2Þ

The following example illustrates an application of the critical temperature method.

9.2.2. Shear resistanceCalculating the shear resistance of a steel cross-section in fire follows the same procedure asat ambient temperature, i.e. the shear resistance of the cross-section is that of the web. In

The plastic bending moment capacity of the cross-section is Mpl;t;RD ¼ 96:389 kN.m

Method 2: Equation (9.1)The plastic modulus of the cross-section is 1453 cm3. The plastic bending moment capa-city of the cross-section is:

Mpl;t;RD ¼ ð0:17� 0:275� 1453Þ=0:7 ¼ 97:04 kN:m

For this cross-section and the specific temperature distribution, the two methods givealmost identical answers. In general, the alternative method (equation (9.1)) has beenfound to be reasonably accurate. The usefulness of the more complex plastic bendingmoment capacity method is when dealing with cross-sections with very steep non-uniform temperature distributions – for example, shelf angle beams or slim floor beams.

Example 9.2: Critical temperature methodCalculate the critical temperature of the cross-section used in Example 9.1. Assume thatthe applied maximum bending moment in the beam at the fire limit state is equal to theplastic bending moment capacity calculated using method 2 in Example 9.1 above.

Calculation resultsThe degree of utilization is:

�0 ¼ 0:7� 97:04=ð0:275� 1453Þ ¼ 0:17

Equation (9.2) gives �a;cr ¼ 749:48C. This critical temperature is identical to the maximumtemperature of 7508C used in Example 9.1. This is not surprising as the critical tempera-ture–degree of utilization relationship (equation (9.2)) is the result of curve-fitting the steeleffective yield strength–temperature relationship given in Table 6.1.

85

CHAPTER 9. DESIGN OF BENDING MEMBERS


clause 4.2.3.3(6), the reference temperature of the web is defined as the average temperatureof the web. This is an approximation because, strictly speaking, the averaging process shouldbe applied on the steel design strength of the web, instead of the temperature of theweb. However, averaging the steel design strength of the web would be more laborious. Thefollowing worked example can be used to show the difference of the two averaging processes.

9.2.3. Lateral torsional bucklingLateral torsional buckling should rarely be a problem for steel beams at the fire limit state.The calculation methods in EN 1993-1-2 are briefly described for completeness.

9.2.3.1. Steel beam with uniform temperature distribution in the cross-sectionFor a beam with uniform temperature distribution in the cross-section, calculating the lateraltorsional buckling resistance of the beam at fire limit state follows the same procedure as atambient temperature in EN 1993-1-1. But there are two modifications: (1) the slenderness ofthe beam should be modified to take account of the difference in reduction factors in the yieldstrength and modulus of elasticity of steel at elevated temperatures; (2) the strength reductionfactor for lateral torsional buckling at fire limit state follows equation (8.3) instead of any ofthe buckling curves in EN 1993-1-1. Both modifications are identical to steel columns whichhave already been described in Section 8.3.

9.2.3.2. Steel beam with non-uniform temperature distribution in the cross-sectionWhen temperature distribution in the cross-section of a steel beam is non-uniform, thecalculation method for checking lateral torsional buckling resistance is the same as for abeam with uniform temperature distribution, but the maximum temperature of the compres-sion flange �a;com should be used as the reference uniform temperature of the beam. This willbe conservative when the compression flange of the cross-section has the highest tempera-ture. But this method may not be safe if the compression flange of the cross-section hasthe lowest temperature.

9.2.4. Control of deformationThe fundamental objective of fire safety design is to prevent fire spread. For a load-bearingmember, the main design criterion is to avoid structural collapse, therefore the designstrength of the member is the main consideration of the Eurocodes. However, for some

Example 9.3: Calculation of sheer resistanceCalculate the shear resistance of the cross-section in Example 9.1.

Calculation results(1) Using average temperature of the webThe average temperature of the web is:

12 � ½ð550þ 750Þ=2þ 750� ¼ 7008C

giving the reduction factor for the yield strength of steel ky;�;web ¼ 0:23 according to Table6.1.

(2) Using average steel design strength of the webAssume the web is divided into three parts as in Example 9.1. The average reduction factorfor the yield strength of steel of the web is:

ky;�;web ¼ 12 � ½ð0:47þ 0:23Þ=2þ 0:17� ¼ 0:26

Calculating the average web temperature can be troublesome because it will benecessary to know the temperature distribution in the entire web. Since shear resistanceusually does not govern design, it is safe to assume that the web temperature is thesame as that of the heated flange.

86



beams, deformation may also have to be controlled. For example, deflection control becomesimportant for the following two cases:

(1) Large beam deflections cause the fire protection material to undergo large strains, whichmay become brittle and detach from the steel beam.

(2) Large beam deformation may lead to openings in the separating members underneaththe beam, leading to fire integrity failure of the fire-resistant compartment.

It is likely that the beam deformation limits for the above two cases will be different. Ifdesign is concerned with performance of the fire protection material, the deformationlimit should correspond to the maximum steel strain that would make the fire protectionmaterial ineffective. In general, commonly used fire protection materials can accommodatelarge steel strains so that the full steel strength can be sustained. However, if a fire protectionmaterial cannot accommodate large strains, the steel design strength should be reduced tothat corresponding to the appropriate maximum strain level of the fire protection material.

For the second case, how much a steel beam can deform without breaching fire integrity ofthe fire resistant compartment has never been properly considered. But in light of recentadvances in structural fire engineering in which structural deformations can approach verylarge values without causing a structural collapse, fire safety design based on structuralstrength alone may not be adequate and it may be necessary to explicitly check structuraldeformations. To do so, it will be necessary to employ advanced calculation methodsbecause the simplified calculation methods in the various Eurocodes cannot perform thistask.

9.3. Steel beam exposed to fire on three sides with concreteslab on the fourth sideA steel beam exposed to fire on three sides with concrete slab on the fourth side may bedesigned either as a steel beam or as a composite beam. Section 9.2 has described thedesign for steel beams. This section will provide additional guidance if the beam is designedas a composite beam.

For this type of composite beam, there is no need to check for lateral torsional buckling(clause 4.3.4.1.1) because under sagging bending moment, the compression flange of thebeam is restrained by the concrete slab. Under hogging bending moment in a continuousbeam near a support, the unrestrained length of the beam will likely be short and thebending moment gradient is steep.

The vertical shear capacity of a composite beam (clause 4.3.4.1.3) is taken as the shearresistance of the steel section, which has already been described in Section 9.2.2 above.

A composite beam should have adequate longitudinal shear capacity at the interfacebetween the concrete slab and the steel profile. The calculation method (clause 4.3.4.1.5 inEN 1994-1-2) is the same as in EN 1994-1-1 for a composite beam at ambient temperature,but the compressive capacity of the concrete slab and the tensile capacity of the steel profileshould account for non-uniform temperature distributions in the concrete slab and the steelprofile.

The sagging and hogging bending moment capacity of a composite cross-section may becalculated by using the plastic theory for any class of cross-section except for class 4 cross-section under hogging bending moment (clause 4.3.4.1.2). The calculation procedure is thesame as at ambient temperature in EN 1994-1-1, but should use the relevant material proper-ties at elevated temperatures, considering non-uniform temperatures in the concrete slab, thesteel profile and reinforcement.

In order to facilitate the above calculations for longitudinal shear capacity and bendingmoment capacity, it is necessary to have data on shear resistance of the stud shear connectorsin fire. EN 1994-1-2 provides simple recommendations to relate temperatures of the studconnectors and concrete to that of the upper flange of the steel profile. These temperaturesare then used to obtain the reduced material strengths of the stud shear connectors and

87



concrete, which are then substituted into relevant equations in EN 1994-1-1 to give thereduced shear resistance of the stud shear connectors.

Alternatively, the critical temperature method may be used to estimate the critical tem-perature of the lower flange of the composite beam under a given sagging bendingmoment. This method is very simple and can be used to quickly estimate whether the com-posite beam is adequate in fire without going through the detailed calculations described inthis section. However, for a composite beam designed for partial shear connection atambient temperature, using the critical temperature method is likely to underestimate theresistance of the composite beam. This comes about because the critical temperaturemethod does not take into account the better performance of the stud shear connectorsthan the steel profile. If this is the case, and should clause 4.3.4.2.3 of EN 1994-1-2 indicatethat the composite beam with partial shear connection is slightly inadequate, the currentversion of BS 5950 Part 812 may be used to give a higher critical temperature. However,to ensure consistency in the use of design codes, the designer should still perform detailedcalculations using EN 1994-1-2 to prove that the composite beam does have sufficientresistance in fire.

9.4. Composite beams comprising steel beams with partialconcrete encasementTwo methods may be used to calculate the bending resistance of a composite beamcomprising a steel section with partial concrete encasement. In the first method, the tem-perature distribution in the composite cross-section should be known, either from fire testsor from numerical modelling. The plastic analysis method, as described in Section 9.2.1 andillustrated in Example 9.1, may be used, taking into consideration reduced strengths of thesteel profile, the concrete and the reinforcing bars at the respectively elevated temperatures.

The alternative method, which is given in Annex F, is only applicable to standard fireexposure beneath the concrete slab. In the alternative calculation method, there is no needto calculate the temperature distribution in the composite cross-section. Instead, thecomposite cross-section is divided into a few blocks, each having the same mechanicalproperties. For calculating the sagging moment resistance (refer to Fig. 9.2), the compositecross-section is divided into the following parts:

. concrete section: with a reduced thickness and the same design strength as at 208C

. upper flange of the steel profile: with a reduced effective width and the same designstrength as at 208C

x

_+

_

+

2

1 3

(b)

(a)

kafay / γM,fi,a

krfry / γM,fi,s

fay,x / γM,fi,a

fay / γM,fi,a

fc / γM,fi,c

u2

us

u1,3

bfi

bc

hc

hc,h

hc,fi

hh

h l

bfi ef

ew

beff

b

h

Fig. 9.2. Elements of a partially encased composite cross-section for calculation of the sagging momentresistance: (a) example of stress distribution in concrete; (b) example of stress distribution in steel

88



. top part of the web: with the same design strength of steel as at 208C

. bottom part of the web: with a reduced design strength of steel

. lower flange of the steel profile: with a reduced design strength of steel

. reinforcing bars in the concrete between the flanges of the steel profile: with a reduceddesign strength.

For calculating the hogging moment resistance (refer to Fig. 9.3), the composite cross-section is divided into the following parts:

. reinforcing bars in the slab: with reduced design strengths depending on fire resistancerating and positions of the reinforcing bars

. upper flange of the steel profile: as for calculating the sagging moment resistance

. concrete between the flanges of the steel profile: with a reduced cross-section but the samedesign strength of concrete as at ambient temperature

. reinforcing bars in the concrete between the flanges of the steel profile: as for calculatingthe sagging moment resistance.

The concrete slab, the web and lower flange of the steel profile should be ignored.To check the vertical shear resistance of the steel web, the steel design strength distribution

as for calculating the sagging moment resistance should be used.The shear connectors may be assumed to retain their full strength of ambient temperature

provided they are fixed directly to the effective width of the upper flange of the steelprofile.

A worked example is provided below (Example 9.4) to illustrate the calculation method inAnnex F.

(a)

(b)

krfry / γM,fi,s

ksfsy / γM,fi,s

fay / γM,fi,a

fc / γM,fi,c

3b

hc

hfi

bc,fi

bfi

bc

bc,fi

bfi

b

h

+

+

-

-

-

-

ew

ef ul

uh

Fig. 9.3. Elements of a partially encased composite cross-section for calculation of the hogging momentresistance: (a) example of stress distribution in concrete; (b) example of stress distribution in steel

Example 9.4: Use of Annex FFigure 9.4 shows the dimensions of a partially encased composite beam cross-section.The required standard fire resistance rating is R60. The steel grade is S275 and thecylinder strength of concrete is 25N/mm2. The design strength of the reinforcing barsis 460N/mm2. The partial safety factor for materials is 1.0. Calculate the saggingbending moment resistance and shear resistance of the cross-section.

Calculation results(1) Concrete slabFrom Table F.1, the reduction in slab thickness is hc;fi ¼ 20mm. The effective thickness ofthe slab is 200� 20 ¼ 180mm.

89



80

40

457

190.4

200

2000

T24

ef = 14.5

ew = 9

Fig. 9.4. Dimensions used in Example 9.4 (units in mm)

(2) Upper flange of the steel profileFrom Table F.2, the reduction in flange width is:

bfi ¼ 14:5=2þ 10 ¼ 17:25mm

The effective width of the upper flange is:

190:4� ð2� 17:25Þ ¼ 155:9mm

The tensile capacity of the upper flange is:

Ra;uf ¼ 155:9� 14:5� 275=1000 ¼ 621:6 kN

(3) Top part of the web

h=bc ¼ 457=190:4 ¼ 2:4

Table F.3 gives a1 ¼ 9500mm2 and a2 ¼ 0. Therefore

hl ¼ 9500=190:4 ¼ 49:9mm

hh ¼ 457� ð2� 14:5Þ � 49:9 ¼ 378:1mm

The tensile capacity of the top part of the web is:

Ra;uw ¼ 378:1� 9:0� 275=1000 ¼ 935:8mm

(4) Bottom part of the web

a0 ¼ 0:018� 14:5þ 0:7 ¼ 3:31

Table F.4 gives:

ka ¼ ½0:21� 26=190:4þ 457=ð24� 190:4Þ� � 3:31 ¼ 0:57 > ka;max ¼ 0:4

Therefore ka ¼ 0:4.The tensile capacity of the bottom part of the web is:

Ra;lw ¼ 49:9� 9:0� ð1þ 0:4Þ=2� 275=1000 ¼ 86:5 kN

The centre of this tensile capacity is 21.4mm from the bottom of the web.

(5) Lower flange of the steel profileThe tensile capacity of the lower flange is:

Ra;lf ¼ 190:4� 14:5� 0:4� 275=1000 ¼ 303:7 kN

(6) Additional reinforcing bars

Am=V ¼ ð2� 457þ 190:4Þ=ð457� 190:4Þ ¼ 0:01269mm�1

From equation (F.2)

u ¼ 1=½1=80þ 1=40þ 1=ð190:4� 9:0� 40Þ� ¼ 22:4mm

90



9.5. Reinforced concrete beamEN 1992-1-2 provides two calculation methods for reinforced concrete beams. The firstcalculation method can be used on its own while the second calculation method should beused in conjunction with the tabulated data. The first calculation method is based on thereduced concrete cross-section that is obtained either from the 5008C isotherm method orthe zone method, which have already been described in Section 8.5. Once the reduced con-crete cross-section is determined, the bending moment capacity of the cross-section maybe calculated in the same way as in EN 1992-1-1 for reinforced concrete beams at ambienttemperature.

When checking the shear and torsion capacity of a reinforced concrete beam at fire limitstate, the reference link temperature should be taken as that at the intersection of the linkswith the limit line of the effective tension area of the reduced cross-section that is calculatedaccording to EN 1992-1-1.

The second calculation method is given in Annex E of EN 1992-1-2. This method is used toextend scope of application of the tabulated data in Section 5 of EN 1992-1-2. The tabulateddata give the minimum dimensions of reinforced concrete beams and the minimum concretecover to reinforcement. When using the method in Annex E of EN 1992-1-2, the minimumdimensions of the reinforced concrete beams cannot be changed. Therefore, Annex E shouldonly be used when it is necessary to justify reducing the concrete cover to reinforcement (axisdistance aÞ in the tabulated data. Furthermore, this calculation method should only beapplied where the applied load is predominantly uniformly distributed.

From Table F.5:

kr ¼ ð22:4� 0:034� 0:04Þ � 0:101=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0:01269

p¼ 0:647

The total area of 2T24 bars is 904.8mm2, therefore the tensile capacity of the reinforcingbars is:

Rs ¼ 904:8� 0:647� 460=1000 ¼ 269:3 kN

Sagging bending moment resistanceThe total tensile capacity of the steel profile and reinforcing bars is:

Rs ¼ 621:6þ 935:8þ 86:5þ 303:7þ 269:3 ¼ 2261:9 kN

The compression capacity of the effective concrete slab depth is:

Rc ¼ 2000� 180� 0:85� 25=1000 ¼ 7650 kN > 2261:9 kN

The depth of concrete in compression is:

dc ¼ 2261:9=7650� 180 ¼ 53:22mm

Taking moments about the top of the concrete slab, the sagging bending momentresistance of the partially encased composite cross-section is:

Mfi;t;Rd ¼ � 2261:9� 53:22=2=1000þ 621:6� ð200þ 14:5=2Þ=1000

þ 935:8� ð200þ 14:5þ 378:1=2Þ=1000þ 86:5

� ð200þ 457� 14:5� 21:4Þ=1000þ 303:7

� ð200þ 457� 14:5=2Þ=1000þ 269:3� ð200þ 457� 14:5� 80Þ=1000

¼ 848:7 kN:m

Shear resistanceThe shear resistance of the steel web is:

935:8þ 86:5ffiffiffi3

p ¼ 590:2 kN

91



9.6. Comments on EN 1992-1-2 tabulated dataTabulated data for reinforced concrete beams are given inTables 5.5–5.7 of EN1992-1-2. Table5.5 is for simply supported beams made with reinforced and prestressed concrete, Table 5.6 forcontinuous beams made with reinforced and prestressed concrete. For reinforced and pre-stressed concrete continuous I-beams with high shear (clause 5.6.3(6)), the minimum beamwidth and web thickness are given in Table 5.7.

The tabulated data are based on critical steel temperatures of 5008C for conventionalreinforcing bars (clause 5.2.(4)), 4008C for prestressing tendons and 3508C for strands andwires (clause 5.2(5)), corresponding to a reduction factor for the design load level for thefire situation (clause 2.4.2) of �fi ¼ 0:7. If the design load level is different, EN 1992-1-2allows the axis distance of the reinforcing bars to be changed (clause 5.2(7) and clause5.2.(8)). Furthermore, if the critical steel temperature is lower than 4008C, the minimumcross-sectional dimensions should be increased (clause 5.2(10)).

92



CHAPTER 10

Design of slabs

10.1. IntroductionThis chapter provides guidance on the design of fire-resistant composite slabs according toEN 1994-1-2 and reinforced concrete slabs according to EN 1992-1-2.

A fire-resistant slab may be divided into two generic types: non-load-bearing andload-bearing. A non-load-bearing fire-resistant slab should meet the fire-resistant require-ments of sufficient thermal insulation and integrity. A load-bearing fire-resistant slabshould also meet the fire-resistant requirement of sufficient load-carrying capacity, inaddition to thermal insulation and integrity. At present, it is difficult to evaluate fire integrityby calculation. It is assumed that if the fire safety design follows the tabulated data or thesimplified calculation methods presented in EN 1994-1-2 or EN 1992-1-2, the designwould meet the fire-resistant requirement of integrity and no further check is necessary. Ifadvanced calculation methods are used, the designer should ensure that the integrity ofthe fire-resistant compartment is maintained by appropriate detailing, so that the largestructural deformations may be accommodated by the fire-resistant compartment. As withdealing with other types of structural member, this chapter will only provide guidance onusing simplified calculation methods.

10.2. Composite slabsTo check for both fire-resistant requirements of thermal insulation and load-bearing capacityof a composite slab, it is essential that temperatures in the slab are available. The main focusof the design clauses in EN 1994-1-2 is on providing equations to calculate temperatures indifferent parts of a composite slab. These equations (Annex D of EN 1994-1-2) were derivedby Both36 who curve-fitted the results of extensive numerical simulations using the finite-element software DIANA. Detailed equations are given in section 4.5 of this guide.

The calculation method in Annex D is applicable to slabs with both re-entrant andtrapezoidal steel decking profiles. The range of applicability in clause 4.3.2(8) of EN 1994-1-2 is based on an inventory of commonly used steel decking types. Concrete can be eithernormal weight or lightweight. Although not mentioned in EN 1994-1-2, the average moisturecontent was 4% for normal-weight concrete and 5% for lightweight concrete, by dry weight.Since higher moisture content will reduce the concrete temperatures, Annex D may besafely applied to concrete with higher moisture contents. However, if the concrete moisturecontent is significantly below the assumed levels, additional thermal analysis may benecessary. An important assumption (not clearly mentioned in Annex D of EN 1994-1-2)by Both36 is that the steel decking remains fully bonded to the concrete. Steel decking hasbeen observed to debond in some fire tests. Therefore, if it is considered that the steeldecking would debond in fire, its contribution to the bending moment resistance of theslab should not be included.


The following worked examples illustrate the step-by-step implementation of the designrecommendations in Annex D of EN 1994-1-2.

Example 10.1: Load carrying capacity of composite slabFigure 10.1 shows the dimensions of the unit width cross-section of a continuouscomposite slab using trapezoidal steel decking. It is required to calculate the load-carryingcapacity of the composite slab under uniformly distributed load in fire.

55

70

120

6060

300

Fig. 10.1. Dimensions of unit width of slab (in mm)

Input data

Slab span: L ¼ 4:5mFire-resistance rating: 60minSteel decking thickness: 1mmSteel decking grade: S355 cold-formedConcrete grade: C30, normal weight, �M;fi;c ¼ 1:1Top reinforcement: A193mm2/m mesh, axis distance¼ 20mmAdditional reinforcement: T12 in each rib, axis distance¼ 30mmReinforcement grade: 460N/mm2

Calculation results

From the dimensions in Fig. 10.1, the geometric dimensions of Figs 4.4 and 4.5 can becalculated as:

l1 ¼ 180mm, l2 ¼ l3 ¼ 120mm, h1 ¼ 70mm, h2 ¼ 55mm, � ¼ 61:4 degrees

(Note: these dimensions fall outside the range of applicability of the calculation method inAnnex D. However, the following calculations are still performed using this calculationmethod for the purpose of illustrating the application of the design method.)

A ¼ 55� 180þ 120

2

� �¼ 8250mm2:m=m

Lr ¼ 120þ 2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi552 þ 180� 120

2

� �2s

¼ 245:3mm2:m=m

A

Lr

¼ 33:63mm;� ¼ 0:809

u1 ¼ u2 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi302 þ 602

p¼ 67:08mm, u3 ¼ 30mm, equation (4.1) giving z ¼ 2:343mm0:5

(1) Fire resistance according to thermal insulationUsing equation (D.1) and Table D.1 (from Annex D) for normal-weight concrete

94



gives:

ti ¼ �28:8þ 1:55� 70� 12:6� 0:809þ 0:33� 33:63� 735=120þ 48� 33:63=120

¼ 88

(which is greater than 60min and so OK)

(2) Sagging moment resistance Mfi;Rdþ

Steel decking lower flange:

Equation (D.4) and Table D.2 (of Annex D) give:

� ¼ 951� 1197=120� 2:32� 33:63þ 86:4� 0:809� 150:7� 0:8092 ¼ 834:48C

Table 6.1 gives strength reduction factor k ¼ 0:093

Area A ¼ 120mm2

Steel decking web:

� ¼ 661� 833=120� 2:96� 33:63þ 537:7� 0:809� 351:9� 0:8092 ¼ 759:28C

Table 6.1 gives k ¼ 0:159, A ¼ 125:3mm2

Steel decking upper flange:

� ¼ 340� 3269=120� 2:62� 33:63þ 1148:4� 0:809� 679:8� 0:8092 ¼ 708:88C

k ¼ 0:219, A ¼ 120mm2

Reinforcing bar in rib:Equation (D.5) and Table D.3 (of Annex D) give:

�s ¼ 1191� 250� 30=55� 240� 2:343� 5:01� 33:63þ 1:04� 61:4� 925=120

¼ 3808C

Table 6.6 gives strength reduction factor k ¼ 0:952

Area ¼ 113:1mm2

Depth of concrete in compression:

Design strength of concrete ¼ 30=1:1 ¼ 27:27N=mm2

Tensile capacity of steel decking and reinforcement bar in rib:

120� 355� 0:093þ 125:3� 355� 0:159þ 120� 0:219� 355þ 113:1� 0:952� 460

¼ 3961:8þ 7072:6þ 9329:4þ 49 529 ¼ 69 893N

Equation (4.2) of EN 1994-1-2 gives the depth of concrete in compression as:

dc ¼ 69893=ð0:85� 300� 27:27Þ ¼ 10:05mm

Taking moment about the centre of compression, equation (4.3) of EN 1994-1-2 givesthe sagging moment resistance as:

Mfi;Rdþ ¼ 3961:8� 70� 10:05=2þ 55� 0:5ð Þ þ 7072:6� 70� 10:05=2þ 55=2ð Þ

þ 9329:4� 70� 10:05=2þ 0:5ð Þ þ 49529 � 70� 10:05=2þ 55� 30ð Þ

¼ 6 195 000N:mm ¼ 6:195 kN:m

(3) Hogging moment resistance Mfi;Rd�

Hogging reinforcement area¼ 193mm2 �m� 0:3m ¼ 57:9mm2

N ¼ 57:9� 460 ¼ 26 634N

Equation (D.7) and Table D.3.3 (of Annex D) give:

�lim ¼ 867� 1:9� 10�4 � 8:75� 33:63� 123� 0:809� 1378=120 ¼ 4578C

95

CHAPTER 10. DESIGN OF SLABS


Equation (D.5) gives:

457 ¼ 1191� 250� 0:75� 240� z� 5:01� 33:63þ 1:04� 61:4� 925=120

giving z ¼ 1:809mm0:5.Equation (D.9) gives:

YI ¼ YII ¼1

1

1:809� 4ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

180þ 120p

� �2¼ 9:65mm < 55mm

Equation (D.10) gives:

XII ¼1

2� 120þ 9:65

sin 61:4cos 61:4� 1ð Þ ¼ 54:27mm

giving a total effective concrete width of 108.54mm at this position.For simplicity, assume the effective width of the concrete in the rib is constant. Equa-

tion (4.2) of EN 1994-1-2 gives the concrete depth in compression as:

dc ¼ 26 634=ð0:85� 108:54� 27:27Þ ¼ 10:59mm

Equation (4.3) of EN 1994-1-2 gives the hogging moment resistance as:

Mfi;Rd� ¼ 26 634� 125� 20� 9:65� 10:59=2ð Þ=1 000 000 ¼ 2:4 kN:m

(4) Load-carrying capacity of the composite slab in fireAccording to plastic analysis and assuming that plastic hinges form at the supports and inthe mid-span of the continuous slab, the slab resistance to uniformly distributed load iscalculated from:

Mfi;Rdþ þMfi;Rd� ¼ 18wL

2

where L ¼ 4:5m, giving w ¼ 3:395 kN/m.The resistance of the slab in fire to uniformly distributed load is

3:395=0:3 ¼ 11:32 kN=m2

Example 10.2: Use of Annex DUnprotected composite slab with profiled steel decking. Fire design for standard fireexposure in accordance with the informative Annex D of EN 1994-1-2: 2005.

Assumed design parameters

Span ¼ 3.5mSlab thickness ¼ 140mmConcrete type lightweightCylinder strength fck ¼ 30N/mm2

Deck yield strength fa ¼ 280N/mm2

Mesh A252Mesh yield strength fy ¼ 500N/mm2

Cover ¼ 15mmFire resistance 120min

Consider the deck profile as follows:

l1 ¼ 112:5mm; l2 ¼ 137:5mm; l3 ¼ 40:0mmh1 ¼ 89.0mm; h2 ¼ 51.0mm; h3 ¼ 0.0mm

96



Screed

Concrete

Steel sheeth2

l2

l1

h1

h3

l3

Fig. 10.2. Deck profile

Assumed design actions

Dead loads:

Selfweight of slab ¼ 2.61 kN/m2

Ceiling and services ¼ 0.9 kN/m2

Total permanent action, Gk ¼ 3:51 kN=m2

Imposed loads:

Occupancy load ¼ 2.5 kN/m2

Movable partitions ¼ 0.8 kN/m2

Total variable load, Qk ¼ 3:3 kN=m2

Design effect at ambient temperature:

Ed ¼ 1:35ð3:51Þ þ 1:5ð3:30Þ ¼ 9:69 kN/m2

Design action in fire:Combination factor 1;1 ¼ 0.5 for Category B: Office area (EN 1990, Tables NA.A1.1 and

NA.A1.2 (A))

Partial factors for actions �G ¼ 1.35; �Q;1 ¼ 1.5The reduction factor

�fi ¼Gk þ 1;1Qk;1

�GGK þ �Q;1Qk;1

¼ 0:55 (EN 1994-1-2, 2.4.2(3))

Design action in fire

Efi;d;t ¼ �fiEd ¼ 5:33 kN=m2(EN 1994-1-2, 2.4.2(2))

Check for application limitations (EN 1994-1-2, Table D.7):l1 ¼ 112.5mm within the limits 77:0�135:0mm ) OKl2 ¼ 137.5mm within the limits 110:0�150:0mm ) OKl3 ¼ 40.0mm within the limits 38:5�97:5mm ) OKh1 ¼ 89.0mm within the limits 50:0�130:0mm ) OKh2 ¼ 51.0mm within the limits 30:0�60:0mm ) OK

Thermal insulation (EN 1994-1-2, D.1(2), equation (D.3)):

Configuration factor � of the upper flanges is given by:

� ¼ 1

l3

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih22 þ l3 þ

l1 � l22

� �2s�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih22 þ

l1 � l22

� �2s24

35

¼ 1

40

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi512 þ 40þ 112:5� 137:5

2

� �2s�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi512 þ 112:5� 137:5

2

� �2s24

35

¼ 0:136

97



The rig geometry factor A=Lr is given by (EN 1994-1-2, equation (D2)):

A

Lr

¼ h2ðl1 þ l2Þ=2l2

¼ 51ð112:5þ 137:5Þ=2137:5

¼ 6375

137:5¼ 46:36mm

(Note: Lr is the exposed area of the rib per metre of rib length which is taken as the upperflange in this case.)

For lightweight concrete (Table D.1):

a0 ¼ �79:2min; a1 ¼ 2:18min/mm; a2 ¼ �2:44min; a3 ¼ 0:56min/mm;a4 ¼ �542mmmin; and a5 ¼ 52:3min.

Fire resistance with respect to thermal insulation ti (in min) is given by (equation (D.1)):

ti ¼ a0 þ a1h1 þ a2�þ a3A

Lr

þ a41

l3þ a5

A

Lr

1

l3

¼ �79:2þ 2:18� 89� 2:44� 0:136þ 0:56� 46:36� 542

40þ 52:3� 46:36

40

¼ 187:5min > 120min

Load-carrying capacity

The sagging and hogging moment capacities must be calculated and compared with thefree bending moment.Free bending moment M0 is given by:

M0 ¼L2

8Efi;d;t ¼

3:52

8� 5:33 ¼ 8:16 kNm per metre width

Sagging moment resistance Mfi;Rdþ

Temperature factors for lower flange (LWC and R120):

b0 ¼ 10628C; b1 ¼ �3998Cmm; b2 ¼ �0:658Cmm;

b3 ¼ 19:88C; and b4 ¼ �43:78C (Table D.2)

Temperature of lower flange �a;LF is given by (equation (D.4)):

�a;LF ¼ b0 þ b11

l3þ b2

A

Lr

þ b3�þ b4�2

¼ 1062� 399

40� 0:65� 46:36þ 19:8� 0:136� 43:7� 0:1362

¼ 1023:88C

Temperature factors for web (LWC and R120):

b0 ¼ 9898C; b1 ¼ �6298Cmm; b2 ¼ �1:078Cmm;

b3 ¼ 186:18C and b4 ¼ �152:68C (Table D.2)

Temperature of web �a;web is given by (equation (D.4)):

�a;web ¼ b0 þ b11

l3þ b2

A

Lr

þ b3�þ b4�2

¼ 989� 629

40� 1:07� 46:36þ 186:1� 0:136� 152:6� 0:1362

¼ 946:18C

98



Temperature factors for upper flange (LWC and R120):

b0 ¼ 9038C; b1 ¼ �15618Cmm; b2 ¼ �0:928Cmm;

b3 ¼ 305:28C; and b4 ¼ �197:28C (Table D.2)

Temperature of upper flange �a;UF is given by (equation (D.4)):

�a;UF ¼ b0 þ b11

l3þ b2

A

Lr

þ b3�þ b4�2

¼ 903� 1561

40� 0:92� 46:36þ 305:2� 0:136� 197:2� 0:1362

¼ 859:28C

Effective depth:

h2h1

¼ 51

89¼ 0:57 < 1:5; h1 ¼ 89 > 40mm (equation (D.4(1))

heff ¼ h1 þ 0:5h2l1 þ l2l1 þ l3

� �¼ 130:8mm (equation (D.15a))

Plastic neutral axis:

152.5 mm

51 mm

89 mmheff = 130.8 mm

+

–

z

Np

xpl Nc

Fig. 10.3. Plastic neutral axis

Tensile resistance of steel deck is given by (4.3.1):

Np ¼Xni¼1

Aiky;�;ify;i

�M;fi;a

� �

¼ 1:2� 137:5� 0:035þ 2� 52:5� 0:051þ 40� 0:08ð Þ � 280=1000

¼ 4:50 kN per 152:5mm

¼ 29:5kN per metre width

Assuming that the top layer of concrete slabs are at a temperature below 3008C, thedepth of concrete slab in compression xpl is given by:

�slab Ajkc;�;�fc;j

�M;fi;c

� �¼ Np

0:85� 30� 1000� xpl ¼ 29:52� 1000

xpl ¼ 1:16mm

As can be seen from Table D.5, this area of concrete is at a sufficiently low temperature forfull strength to be assumed.

Lever arm Z:

Z ¼

�Xni¼1

Aiky;�;izi

�fy;i

�M;fi;a

��Np

¼ 117:02mm

99



Sagging moment capacity:

Mfi;Rdþ ¼ NpZ ¼ 29:52� 117:02=1000 ¼ 3:45 kNm per metre width

Hogging moment resistance Mfi;Rd�

Normal force in hogging reinforcement:

Ns ¼ 252� 500=1000 ¼ 126 kN per metre width

Limiting temperature: (equation (D.7))

�lim ¼ d0 þ d1Ns þ d2A

Lr

þ d3�þ d41

l3

¼ 1213� 2:5� 10�4 � 126 000� 10:09� 46:36� 214� 0:136� 2320=40

¼ 626:68C

z-factor: (D.3(6), equation (D.6))

u1 ¼ 89.8mm; u2 ¼ 89.8mm;

u3 ¼ 0:75� h3 ¼ 38.25mm (according to D.3(6))

1

z¼ 1ffiffiffiffiffi



u3p ¼ 0:373

u1 u2

u3

Fig. 10.4. Calculation of z factor

YI ¼1

1

z� 4ffiffiffiffiffiffiffiffiffiffiffiffiffi

l1 þ l3p

� �2 ¼ 419:3mm > h2ð¼ 51mmÞ (D.3(5))

In the case of YI > h2, the ribs of the slab may be neglected. Table D.5 may be used toobtain the location of the isotherm of the limiting temperature �lim as a conservativeapproximation.For �lim ¼ 626.68C, the depth x ¼ 20:1mm (D.3(7))

(Note: for lightweight concrete, the temperatures of Table D.5 are reduced to 90% ofthe values given.) (D.3(9))

152.5 mm

–z

Ns

xpl

h1 = 89 mm

x = 20.1 mm

Fig. 10.5. Depth of limiting temperature isotherm

Depth of concrete slab in compression xpl:

xpl ¼126

0:85� 30¼ 4:94mm

100



10.3. Reinforced concrete slabsThe simplified calculation method in EN 1992-1-2 is based on the reduced slab size in whichthe fire-damaged concrete zone of the slab is obtained in exactly the same way as described inSection 8.5. Afterwards, the slab design calculations follow EN 1992-1-1, but using concretemechanical properties at the relevant elevated temperature.

The following worked example shows how to calculate the reduced slab thickness usingboth the zone method and the 5008C isotherm method.

Level arm, Z ¼ h1 � cover� x�xpl

2¼ 89� 19� 20:1� 4:94

2¼ 47:46mm

Hogging moment capacity:

Mfi;Rd� ¼ NsZ ¼ 126� 47:46=1000 ¼ 5:98 kNm per metre width

Capacity check

Internal spans:

Mfi;Rdþ þMfi;Rd� ¼ 3:45þ 5:98 ¼ 9:43 >M0 ¼ 8:16 kNm per metre width (OK)

End spans:

Mfi;Rdþ þMfi;Rd�

21�Mfi;Rd�

8M0

� �¼ 6:17 <M0 ¼ 8:16 kNm per metre width

(Unsatisfactory)

The end spans therefore require additional reinforcement. The capacity may be increasedby providing additional wires in the ribs to increase the sagging moment capacity.

Example 10.3: Calculation of reduced slab thicknessCalculate the reduced thickness and design strength of concrete for a solid concrete slab infire. The design standard fire resistance rating is 90min. The original slab thickness is100mm.

Calculation results

(1) Using the zone methodThe slab is heated from one side so the half-thickness of the equivalent wall (w1 inFig. 8.6(b)) is the thickness of the slab, w ¼ 100mm.

Divide the slab thickness into four zones, each 25mm in thickness. The distances fromthe centres of the four zones to the exposed surface of the slab are 12.5mm, 37.5mm,62.5mm and 87.5mm. According to Fig. 4.7, the temperatures in these zones are7258C, 4208C, 2408C and 1408C. The temperature at the unexposed surface of the slabis �M ¼ 1108C. From Table 6.4 (for siliceous NWC), the strength reduction factors forthese zones are 0.2625, 0.72, 0.91 and 0.98. The strength reduction factor for the unex-posed surface of the slab is kcð�MÞ ¼ 0:995.

From equation (8.17), the mean reduction coefficient for the slab is:

kc;m ¼ 1� 0:2=4ð Þ4

0:2625þ 0:72þ 0:91þ 0:98ð Þ ¼ 0:682

From equation (8.18), the width of the fire-damaged zone for the slab is:

az ¼ 100 1� 0:682

0:995

� �¼ 31:5

The reduced thickness of the slab is 100� 31:5 ¼ 68:5mm.

101



Afterwards, EN 1992-1-1 should be followed, but using the above reduced thickness ofthe slab and the reduced design strength of concrete, which is 0.995 times that at ambienttemperature.

(2) Using the 5008C isotherm methodUsing Fig. 4.7, the distance of the 5008C isotherm from the exposed surface is 30mm. Thisthickness should be ignored and the reduced thickness of the slab is 100� 30 ¼ 70mm.Slab design should follow EN 1992-1-1, but using the reduced slab thickness and theconcrete design strength at ambient temperature.

102



CHAPTER 11

Other forms of construction

11.1. IntroductionA number of major research studies have been conducted to investigate the fire resistance ofvarious forms of integrated steel construction where adequate fire protection to the steelworkis provided by existing structural components so that there is no need for extra fireprotection. EN 1994-1-2 contains a number of such systems, for example partially encaseduniversal beams and columns, concrete-filled tubular columns, where concrete acts both aspart of the structural load-bearing system as well as providing fire protection to the steel.However, a number of such forms of construction is not included in EN 1994-1-2 and thischapter provides a description of the following systems: slim floor beams, shelf anglebeams and blocked infilled columns.

11.2. Slim floor beamsA slim floor beam is manufactured by welding a wide steel plate to the bottom flange of auniversal column section. The concrete/composite slab is supported on this additionalplate. Figure 11.1(a) provides an illustration of this system. The Corus asymmetric steelbeam (ASB) system is similar to the slim floor beam system, the difference being that anASB section is rolled as one and no additional welding is necessary (Fig. 11.1(b)). In bothsystems, concrete surrounds the upper flange and web of the steel beam and only thelower flange is exposed to fire. Thus, there is a significant residual strength in the steelbeam. Results from the standard fire resistance tests indicate that this form of constructioncan achieve a standard fire resistance rating of 60min without fire protection.

11.3. Shelf angle beamsA shelf angle beam is manufactured by welding a pair of steel angle sections on both sides ofthe web of a universal beam section. The function of these angle sections is to support theconcrete floor slabs. Figure 11.2 provides an illustration of this form of construction.Under fire conditions, only the lower flange and the lower web are exposed to fire. Theupper flange and the upper web are protected by the concrete floor slabs. The steel anglescan also contribute to the fire resistance of the system. Results of the standard fire resistancetests suggest that this form of construction can achieve at least 30min of standard fireresistance without fire protection.

The standard fire resistance calculation for this form of construction is given in AppendixE of the British Standard BS 5950 Part 8.12 This calculation method is based on plasticanalysis of the steel section and the contribution of the concrete slabs is ignored. Toensure fire protection of the steel section by the concrete slabs, the construction details inSection E.1 of BS 5950 Part 8 should be observed.


Appendix E of BS 5950 Part 8 contains an approximate calculation method to determinethe temperatures in the steel section including the steel angles under the standard fire condi-tion. This method is presented below. In this method, the steel section is divided into sevenblocks as shown in Fig. 11.3.

Block 1 is the lower flange. Its temperature may be calculated using equation (4.1) and thesection factor of the unprotected lower flange given by:

Am

V¼ 2ðBe þ tf Þ

Betf� 2

tfð11:1Þ

where tf is the thickness of the lower flange.

(a)

Screed

Concrete floor slab

(b)

Fig. 11.1. (a) Slim floor beam and (b) asymmetric beam

Angle

Steel section

Concrete slab

Fig. 11.2. Cross-section of shelf angle beam

104



Block 2 is the lower web of the steel section. An analysis of the standard fire resistance testresults indicates that the temperature in block 2 is directly related to the lower flange tem-perature, being slightly modified by the rate of heat conduction to the concrete slab. Therate of heat conduction to the concrete slab is represented by the exposed steel web depthto flange width ratio (De=BÞ. Table 11.1 gives temperatures in the lower web of the steelsection. In Table 11.1, T1 is the temperature of the lower flange of the steel section.

Block 3 is the exposed leg of the angle section. Its temperature is a function of the aspectratio and is given in Table 11.2.

The exact locations of blocks 4, 5 and 6 depend on the location of the 3008C line. If thesteel temperature is below 3008C, it is assumed to retain its full strength. Figure 11.4illustrates the two possible locations of the 3008C temperature line and the definition ofthe three blocks.

Block 2, T2

Block 3, T3

Blocks 4, 5 and 6defined in Fig. 11.4

Block 7, T7

De

De Block 1, T1

Concrete slab

Fig. 11.3. Temperature blocks for shelf angle beams

Table 11.1. Temperature of the exposed web (block 2 in Fig. 11.3) of ashelf angle beam

Exposed web temperature for a fire resistanceperiod of

Aspect ratio 30min 60min 90min

De=B � 0:60:6 < De=B � 0:80:8 < De=B � 1:11:1 < De=B � 1:51:5 < De=B

T1-140T1-90T1-45T1-25T1

T1-90T1-60T1-30T1T1

T1-60T1-30T1T1T1

Table 11.2. Temperature of the exposed angle leg of a shelf angle beam

Exposed angle leg temperature for a fireresistance period of



475510550550550

725745765765765

900910925925925

105

CHAPTER 11. OTHER FORMS OF CONSTRUCTION


Blocks 6 and 7 have temperatures lower than 3008C. Since the full steel strength isretained, no further calculation is necessary.

Temperatures in blocks 4 and 5 are calculated using the following equation:

Tx ¼ TR � Gx but Tx � 3008C ð11:2Þwhere TR is the temperature in the angle root; x is the distance (in mm) from the angle rootand G is the temperature gradient (in 8C/mm) in this region. The temperature gradients are2.38C/mm, 3.88C/mm and 4.38C/mm for the standard fire resistance periods of 30min,60min and 90min respectively.

From equation (11.1), the location of the 3008C is given by:

x ¼ TR � 300

Gð11:3Þ

Values of TR are given in Table 11.3.

Table 11.3. Temperature TR

Value of TR for a fire resistance period of



350385425425425

600620640640640

775785800800800

11.4. Blocked infilled columnsThe fire resistance of a bare steel column is increased significantly if autoclaved aeratedconcrete blocks are placed between the inner faces of the flanges. It is (conservatively)assumed that the blocks do not contribute to the load-carrying capacity of the memberbut provide insulation to the web of the column and the inner surface of the flanges,leading to a reduction in the temperature rise of the steel section. The situation is illustratedin Fig. 11.5.

This solution is suitable for 30min fire resistance provided that the load ratio does notexceed 0.6 and that the section factor does not exceed 69m�1. The limiting values arebased on tests carried out by British Steel and the Building Research Establishment(BRE) and are reported in BRE Digest 317.41 The minimum size of column required toachieve 30min fire resistance is a 203� 203� 52UC and the concrete blocks should have aminimum density of 475 kg/m3 in order to achieve the required level of insulation.

If fire resistance periods in excess of 30min are required, a number of solutions areavailable using partially encased columns and concrete-filled rectangular hollow sections.Details of these methods are provided in a Steel Construction Institute design guide42 andillustrated in Fig. 11.5.

Block 6, T6

Block 5, T5

Block 4, T4

Block 6, T6

Block 5, T5

Block 4, T4300°C

(a) (b)

300°C

Fig. 11.4. Definition of blocks 4, 5 and 6: (a) in angle leg; and (b) above angle

106



(a) (b) (c) (d)

Fig. 11.5. Partially protected columns: (a) blocked-in steel column; (b) partially encased steel column(unreinforced); (c) partially encased steel column (reinforced); and (d) concrete-filled steel section

107

CHAPTER 11. OTHER FORMS OF CONSTRUCTION


CHAPTER 12

Connections

12.1. IntroductionTraditional fire design has been based around the performance of individual elements(beams, columns, walls, floor slabs). The assessment procedures (standard fire tests) donot consider the interaction between structural elements in a realistic steel- or concrete-framed building. The behaviour of connections in a fire or post-fire condition can be criticalin terms of maintaining overall structural stability. The Eurocodes encourage designers toconsider the behaviour of connections explicitly and provide greater flexibility in terms ofavailable design options.

The most common approach to connection design in fire has been to ensure that theavailable cover and minimum dimensions of the connection is at least equivalent to thatof the connected parts (concrete construction) or that the thickness of applied passive fireprotection is at least equal to that used for the connected members (steel and compositeconstruction). However, such an approach fails to consider:

. the applied load level of the connection relative to the connected members

. the ductility required to accommodate the large deformations associated with the firelimit state

. the tensile strength required to resist the large tensile forces generated during the coolingphase of a real fire.

12.2. Concrete connectionsThe design of concrete connections in fire is governed by the same principles and assump-tions that apply to other structural members (beams, columns, walls, floor slabs); that is,fire resistance is a function of the cross-sectional dimensions and the cover to the reinforce-ment. This design philosophy is based on the large thermal inertia of concrete structureswhich is a function of their high mass and low thermal conductivity. Most concreteconnections do not therefore require additional fire protection in order to fulfil themandatory functional requirements.

Detailing of concrete structures is particularly important in relation to performance in fire.A number of authoritative guidance documents are available43;44 that set out detailing rulesfor enhanced performance in fire. These include:

. anchoring reinforcement

. continuous top and bottom reinforcement over supports with effective overlaps toprevent premature failure due to stress reversal

. fire stopping around service penetrations.

Connection performance is subject to the effects of both permanent and variable (dead andimposed load) actions and indirect actions arising from the effects of the fire. In general, the


former do not present any particular design problems as the load levels are generally lower atthe fire limit state. However, indirect actions have a significant impact on the performance ofconnections in fire.

12.2.1. Increase in support moment for continuous structuresThe thermal expansion of the exposed surface of a beam or floor slab induces curvaturewhich has the effect of increasing the support moment on the unexposed face. This maylead to yielding of the top reinforcement if not considered at the design stage. Adequate over-lapping of reinforcement at the support is recommended for reinforced structures. Precaststructures are generally simply supported and have sufficient rotational capacity to dealwith this effect. The effect of thermal curvature is illustrated in Fig. 12.1.

12.2.2. Forces due to restrained thermal expansionWhen a fire compartment is located within a framed structure, the expansion of the heatedelements is restrained by the surrounding cold structure. This restraint to thermal expansionleads to very high compressive forces acting on the connection and has been confirmedthrough large-scale testing. The situation is illustrated schematically in Fig. 12.2. Concreteconnections are likely to be able to accommodate such large forces. However, on cooling,large tensile forces can also be generated and these are not normally taken into account atthe design stage.

12.2.3. Eccentricity of loading due to large deflectionThe effect of large deformations is to increase the eccentricity of loading at the connection.Sufficient rotational capacity must be present to accommodate the large vertical deflectionstypical of exposed floor slabs in a fire situation. Local damage at the support may result fromthe curvature of beams and floors leading to localized failure of the supporting member.

In a framed structure consisting of continuous columns, the horizontal movement of thefloor slab may lead to significant lateral deformation of columns, leading to large stresses andpossible shear failure. This situation is particularly significant on edge columns where theexpansion towards the inside of the building is restrained by the surrounding cold structure.

Fire condition

Normal temperature

Fig. 12.1. Moment distribution in a continuous structure

Fig. 12.2. Compressive forces in a framed structure due to restrained thermal expansion

110



This situation was illustrated in the large-scale fire test undertaken on the European concretebuilding at Cardington (Fig. 12.3).

There is very little guidance in EN 1992-1-2 on the design of joints other than to specifythat the design of joints should be based on an overall assessment of the structural behaviourin fire.

In terms of meeting the insulation requirements for fire resistance, gaps in joints betweenmembers are restricted to 20mm and should not be deeper than half the minimum thicknessof the separating component.

12.3. Steel and composite connectionsConnections (or joints to use the European terminology) to structural steelwork (whethercomposite or not) generally utilize standard connections with standard bolt sizes and platethickness. This simplifies both the design and fabrication process. Guidance on the selectionof appropriate connections is available in established guidance documents produced by theindustry.45�47 In general, connections may be classified as either nominally pinned or fullyfixed depending on their ability to transfer moments from the loaded beams into thecolumns. In reality, all connections are, to some extent, semi-rigid – that is, they havesome measure of rotation capacity and some degree of fixity. One interesting aspect ofconnection behaviour in fire is that connections which are assumed to be simply supportedunder normal conditions actually behave as semi-rigid connections in the event of a fire.

Fig. 12.3. Cardington fire test – lateral movement of edge columns due to restrained thermal expansion

111

CHAPTER 12. CONNECTIONS


The traditional approach to connection design in the UK has been for the structuralengineer to set out the design assumptions in relation to the connections and to leave thedetailed design (end-plate thickness, bolt pitch, etc.) to the fabricator. Connections aregenerally assumed to be simple or moment resisting with simple connections designed toresist shear loads, axial loads and notional moments. The Eurocodes present a more rigorousdesign approach that classifies connections according to strength and stiffness and brings inthe concept of partial strength and semi-rigid connections.

The traditional approach to the design of connections in fire is to ensure there is sufficientpassive fire protection over the connection. In general, this is assumed to mean at least thesame thickness as that on the connected elements (beams and columns); however, theconnection may be loaded to a higher level than the connected parts. As load level isconnected to fire resistance, this may mean insufficient passive fire protection is applied tothe connection. In addition, the connection may have insufficient ductility to accommodatethe large deflections and rotations typical of the fire limit state. Many of the issues discussedabove in relation to concrete connections also apply here. Of particular importance is therotational capacity of the connection, the effects of restrained thermal expansion in generat-ing significant compressive stresses and the tensile capacity of the connection during thecooling phase.

Two methods are given in the fire part of the Eurocode for the design of steel structures,EN 1993-1-2. The first is the simplified procedure set out in clause 4.2.1(6) whereby:

The fire resistance of a bolted or welded connection may be assumed to be sufficient pro-vided that the following conditions are satisfied. (Note: the first condition corresponds to tra-ditional UK design assumptions.)

(1) The thermal resistance (df=�fÞc of the connection’s fire protection should be greater thanthe minimum value of thermal resistance (df=�fÞm of fire protection applied to any of theconnected members.

(2) The utilization of the connection should be less than the maximum value of utlization ofany of the connected members.

(3) The resistance of the connection at ambient temperature should satisfy the recommen-dations given in EN 1993-1-8 (connection design part of EN 1993).

Annex D of EN 1993-1-2 provides an alternative method for calculating the temperaturedistribution through the joint. Once the temperature distribution has been derived then thecapacity in shear, bearing and tension is calculated using appropriate reduction factors toallow for the effects of elevated temperature.

The temperature of the connection in fire is given for beam depths less than 400mm:

�h ¼ 0:88�0½1� 0:3ðh=DÞ�

where:

�h is the temperature at height h (mm) of the steel beam (8C);�0 is the bottom flange temperature of the steel beam remote from the connection (8C);h is the height of the component being considered above the bottom of the beam (mm);

andD is the depth of the beam (mm).

If the depth of the beam is greater than 400mm:

(i) when h is less than D=2:

�h ¼ 0:88�0

(ii) when h is greater than D=2:

�h ¼ 0:88�0½1þ 0:2ð1� 2h=DÞ�

The situation is illustrated in Fig. 12.4.This methodology has been validated against full-scale test data, as shown in Fig. 12.5.

112



In most current design methods the underlying assumption is that the components of theconnection and the supporting members have the same rate of strength reduction. However,this is not necessarily the case. Figure 12.6 compares the strength reduction factors formembers, bolts and welds.

Temperature profile:D < 400 mm

Temperature profile:D > 400 mm

0.88

0.75

0.62

0.88

0.88

0.70

D

h

θh

Fig. 12.4. Thermal gradient within the depth of a composite connection

200

0

400

600

800

1000

0 15 30 45 60 75 90 105 120 135 150Time (min)

Fin plate, experiment

Tem

pera

ture

(°C

)

D1 E1

D2 E2

Fin plate, prediction

Beam, bottom flange

Fig. 12.5. Comparison between Eurocode prediction and test results

1.4

1.2

1.0

0.8

0.6

0.4

0.2

00 200 400 600 800 1000 1200 1400

Temperature (°C)

Red

uctio

n fa

ctor

s

MembersBoltsWelds

Fig. 12.6. Reduction factors for members, bolts and welds

113



From the figure it can be seen that, between 3508C and 10008C, the strength of weldsreduces faster than that of the connecting member. Similarly, between 1008C and 6008Cthe strength of bolts reduces faster than the connected member.

Most practical connections support the applied load by a combination of welds and bolts.It is therefore difficult to say with certainty which of these two components will govern at thefire limit state. Based on the data available, a connection with the same level of fire protectionas the connected member will lose its strength at a faster rate.

However, the temperature profile through a connection is not the same as that of theconnected member. The heating rate tends to be lower through a combination of higherthermal mass at the connection location and the effects of shielding from the connectedmembers. It is concluded that the disadvantages associated with the strength reduction ofbolts and welds are outweighed by the advantages associated with the reduced thermalgradient through the connection. Therefore, the simple rules detailed in the Eurocode donot represent a reduction in existing levels of safety.

The Eurocode connection design procedure is illustratedwith reference to aworked example.

Example 12.1: Major axis beam-to-column connectionConsider the major axis beam-to-column connection illustrated in Figs 12.7 and 12.8.In EN 1993-1-2 two methods are presented for bolted or welded joints. The first is based

on ensuring that the fire resistance of the joint is greater than or equal to that of theconnected members. In general this is a conservative method as the temperature of theconnection is generally less than that of the beams. However, it is also necessary toconsider the utilization of the connection compared to the utilization of the member.As a simplification, the utilization of the joint and the connected members may berelated to the loading and resistance at ambient temperature.

30 90

bb = 150

40

40

p12 = 60

p11 = 60

p13 = 60

tc = 31.4

wb = 7.4

tb = 11.5

wc = 19.1

tb = 8

20

260

30

356 × 171 × 51UB

356 × 171 × 51UB

305

× 3

05 ×

198

UC

6FW all round

hc = 339.9 hb = 353.0

bb = 171.5bc = 314.5

Bolts: M20 8.8Primary beam: S355; Column: S355Plate: A43 (= S275)

Fig. 12.7. Details of major axis beam-to-column connection (all dimensions in mm)

114



A B C D E F

4

3

2

1

9000 9000 9000 9000 9000

6000

9000

6000

Fig. 12.8. Floor layout (all dimensions in mm)

Alternatively, the resistance of the joint may be assessed according to Annex D ofEN 1993-1-2 whereby the temperature of the components are calculated and reductionfactors used to determine the resistance of the joint.

Consider the connection at location E1 in Fig. 12.8.

LoadingThe values of the actions at the fire limit state are given in Table 12.1.

For the purpose of design, the partition load is classed as imposed to account fordemountable partitions. For the fire limit state, the partition load is included in thedead load.

Table 12.1. Actions at the fire limit state

Nature of loading Value (kN/m2Þ

Composite slab 2.06Structural steel sections 0.25Raised floor 0.40Services 0.25Ceiling 0.15Partitions 1.00Imposed 2.50

Permanent actions (G)Uniformly distributed load Gk ¼ 3:11 kN/m2 (4.11 kN/m2 fire limit state)

Variable actions (Q)Uniformly distributed load Qk ¼ 3:50 kN/m2 (2.5 kN/m2 fire limit state)

Loading factors – ambient temperaturePartial factor for permanent actions: �g ¼ 1:35Partial factor for variable actions: �Q ¼ 1:50 (EN 1990, Table A1.2(B))

Loading factors – fire limit stateFor the fire limit state, partial loading factors (�iÞ are not applied to either permanentactions or variable actions.

Combination coefficient for variable action 1 ¼ 0:50 (EN 1990, Table A1.3)Ambient temperature design value of actions

115



. Ultimate limit state

Design UDL, FEd ¼ ð�G � GkÞ þ ð�Q �QKÞ ¼ 9:45 kN=m2

Design moment – primary beamThe design moment on the primary beam is equal to:

MEd ¼ ðR� lÞ=4

where:

R is the end reactions from the secondary beams framing into the primary beambetween gridlines E1 and E2:

R ¼ ½ðl=2Þ � L� FEd� ¼ 255:1 kN

Therefore:

MEd ¼ ðR� lÞ=4 ¼ 382:66 kNm

Design shear force – primary beamThe design shear force is equal to the end reaction on the primary beam.

VEdR=2 ¼ 127:6 kN

Fire limit state design value of actions

. Ultimate limit state accidental design situation

Design UDL, FEd;fi ¼ Gk þ ð 1 �QkÞ ¼ 5:36 (EN1990, Table A1.3)

Design moment – primary beamThe design moment on the primary beam is equal to:

MEd;fi ¼ ðRfi � lÞ=4

where:

Rfi is the end reaction from the secondary beams framing into the primary beambetween gridlines E1 and E2:

Rfi ¼ ½ðl=2Þ � L� FEd;fi� ¼ 144:7 kN

Therefore:

MEd;fi ¼ ðRfi � lÞ=4 ¼ 217 kNm

Design shear force – primary beamThe design shear force is equal to the end reaction on the primary beam.

VEd;fi ¼ Rfi=2 ¼ 72:3 kN

. Method 1:

ðdf=�fÞc � ðdf=�fÞm ðclause 4:2:1ð6ÞÞwhere:

ðdf=�fÞc is the relationship between the thickness of the fire protection material andthe thermal conductivity of the fire protection material for the connection;and

ðdf=�fÞm is the relationship between the thickness of the fire protection material andthe thermal conductivity of the fire protection material for the connectedmember.

116



Resistance of connection – ambient temperature designThe connection (E1) is designed as simply supported at ambient temperature and it isacceptable to carry out the utilization check at ambient temperature. The shear capacityof the connection is assessed using the method detailed in the BCSA/SCI green book46 onsimple connections. The shear capacity of the connection based on the shear capacity ofthe bolt group, the shear capacity of the end plate, the block shear capacity and thebearing capacity of the end plate are summarized in Table 12.2. As the column flange ismuch thicker than the end plate there is no need to consider the resistance of thecolumn flange in bearing.

Table 12.2. End-plate shear and bearing capacity

Resistance check FormulaResistance(kN)

Green book46

page ref.

Shear capacity of bolt group(Fv � �PsÞ

�psAs (or 0:5kbse1tppbsÞ fortop bolt rows

699 93

Plain shear capacity of end plate(Fv=2 � PvÞ

Min (0:6pyAv, 0:7pyKeAvnetÞ 270 94

Block shear (Fv=2 � PrÞ 0:6pytp½Lv þ KeðLt � kDhÞ� 320 94

Bearing (Fv=2 � PbsÞ kbsdtppbs 294 94

Note: symbols used are taken from the BCSA/SCI green book.46 Fv is the design shear force, which equals VEd given inEC3.

Therefore the utilization of the connection is

ðVEd=2Þ=270 ¼ 0:236

This value needs to be compared to the degree of utilization of the beam connected to thecolumn.

Resistance of primary beams – ambient temperature designThe moment capacity of the composite primary beam is:

Mc;Rd ¼ 515 kNm

(Note: this value has been determined following the method given in SCI publicationP055.48 The calculation process is not included in this worked example, as it is concernedwith the design of the connection at the fire limit state.)

Therefore the utilization of the beam is:

MEd=Mc;Rd ¼ 0:74

where MEd is the design moment determined previously.

Determination of fire protection thicknessThe utilization of the beam is greater than that of the connection therefore it is sufficient toensure that the fire protection is at least equivalent to that on the beam. The selection ofthe appropriate beam protection thickness and thermal conductivity can be made on thebasis of the calculation procedure for protected steelwork detailed in Chapter 4.

. Method 2:Annex D of EN 19923-1-2 provides a method for determining the temperature profilewithin the connection. This can then be used to derive reduction factors correspondingto the location of the individual components.

The first step is to calculate the temperature rise of the bottom flange (at mid-span) ofthe connected beam. For this example it is assumed that the required period of fire

117



resistance is 60min and that the applied passive fire protection to be used is 20mmgypsum board applied to three sides of the beam. The relevant formula for protectedmembers is:

��a;t ¼�pAp=V

dpca�a

�g;t � �a;t

1þ �

3

�t� ðe�=10 � 1Þ��g;t ��a;t � 0

and

� ¼cp�pca�a

dpAp

Vðclause 4:2:5:2ð1Þ; equation ð4:27ÞÞ

where:

Ap=v is the section factor for protected steel member (136m�1Þ;ca is the specific heat of the steel (600 J/kgK);cp is the specific heat of the protective material (1700 J/kgK);dp is the thickness of fire protection (0.02m);�a;t is the temperature of the steel at time t (8C);�g;t is the temperature of the gas at time t (8C);�g;t is the increase in gas temperature over the time step t (8C);�p is the thermal conductivity of the fire protection material (0.2W/mK);�a is the density of the steel (7850 kg/m3Þ; and�p is the density of the protection material (800 kg/m3Þ.� ¼ 0:7854

For the standard fire exposure and the specified protection material the temperature ofthe steel beam is calculated as 4458C. The time–temperature relationship is illustrated inFig. 12.9.

100

0

200

300

400

500

600

700

800

900

1000

0 10 20 30 40 50 60

Time (min)

Tem

pera

ture

(°C

) Atmosphere temperatureSteel temperature

Fig. 12.9. Temperature of primary beam (356� 171UB51)

(Note: this is not a particularly efficient design solution. The designer may wish to con-sider rationalizing the fire protection (by using a 15mm board for example) to increase themaximum temperature in the steel beam.)Here the depth of the beam is less than or equal to 400mm, therefore:

�h ¼ 0:88�o½1� 0:3ðh=DÞ� ðD3:1ð4aÞÞwhere:

�h is the temperature at height h (mm) of the steel beam;

118



�o is the bottom flange temperature of the steel beam at mid-span (4458C);h is the height of the component being considered above the bottom of the beam

(mm); andD is the depth of the beam (mm) (355mm).

100

150

0

50

200

250

300

350

400

250 270 290 310 330 350 370 390 410Temperature (°C)

Dis

tanc

e fr

om b

otto

m fl

ange

of b

eam

(m

m)

Bottom flange

Bottom edge of end plate

Bottom bolt row

2nd bolt row from bottom

3rd bolt row from bottom

Top bolt row

Top edge of end plate

Fig. 12.10. Temperature distribution through connection

The temperature of the critical components is illustrated graphically in Fig. 12.10. Thevalues are summarized in the Table 12.3 below.

The temperatures at each location are used to derive reduction factors for the individualcomponents either from Table D.1 for bolts or from Table 3.1 for the end plate andcolumn.

Table 12.3. Temperature of critical components

Description

Distance frombottom flange(mm)

Temperature(8C)

Bottom flange of steel beam at mid-span 0 445Bottom flange of the steel beam in the vicinity of the connection 0 392Bottom edge of end plate 75 367Bottom bolt row 115 3542nd bolt row from bottom 175 3343rd bolt row from bottom 235 314Top bolt row 295 294Top edge of end plate 335 281

The original checks are then repeated using the reduction factors for elevated tempera-ture and compared to the reduced load applied at the fire limit state. In this case the designshear force is reduced according to the fire limit state load factors.

The reduction factors for the individual components are summarized in Table 12.4 andthe corresponding resistance checks are summarized in Table 12.5.

The utilization of the connection at the fire limit state is:

ðVEd;fi=2Þ=270 ¼ 0:14

119



Table 12.4. Reduction factors

ComponentReductionfactor

End plate (based on bottom temperature) 1.0Bottom bolt row 0.832nd bolt row from bottom 0.8853rd bolt row from bottom 0.86Top bolt row 0.933

In this example the connection is utilized less at the fire limit state than at ambienttemperature. This is because the reduction in the applied load at the fire limit state isgreater than the reduction in material properties of the connection components.It should be noted that for moment connections it is more likely that the utilization of

the connection would be higher than that of the connected beam, and that for unprotectedconnections the reduction in the strength of the connection components would be muchgreater.

Table 12.5. Resistance at elevated temperature

Resistance check FormulaResistance(kN)

Shear capacity of bolt group(Fv � �PsÞkb

�psAs � kb (or kb � 0:5kbse1tbpbsÞfor top bolt rows

611

Plain shear capacity of end plate(Fv=2 � PvÞky�

Min (ky;�0:6pyAv, ky;�0:7pyKeAvnetÞ 270

Block shear ðFv=2 � PrÞky� ky;�0:6pytpðLv þ KeðLt � kDhÞÞ 320

Bearing ðFv=2 � PbsÞkb �kbkbsdtppbs 258

Note: the symbols used are taken from the BCSA/SCI green book.46 Fv is the design shear force, which equals VEd;figiven in EC3.

120



CHAPTER 13

General discussion

13.1. IntroductionThe design methodologies presented in the structural Eurocodes provide a framework tofacilitate the performance-based design of structures in fire while enabling accepted prescrip-tive solutions to be adopted where required.

The calculation methods provide a more rational basis for the fire engineering design ofstructures and provide greater flexibility to engineers, architects and end users in relationto the design of new buildings and the refurbishment/reuse of the existing building stock.

In general, this increased flexibility is achieved at the cost of increased design effort. Struc-tural fire engineering covers a wide spectrum of approaches to the nature and effects of theloading and the means of ensuring adequate resistance for the required duration. On the onehand there is a simple reliance on values from published tables based on a simplified assess-ment of both the effects of the fire and the load acting on the structure at the time of the fire.At the other extreme the designer may choose to model the fire using complex computationalfluid dynamics techniques and analyse the entire building using non-linear finite-elementanalysis. The design solution adopted will depend on the particular circumstances of theproject and the requirements of the client and regulatory authorities. It is necessary to con-sider the financial implications of adopting a more sophisticated approach to the design ofstructures in fire. Such methods can only be justified where significant savings in materialor enhanced levels of safety (over and above those required by National regulations) arerequired. The general recommendation is to use the simplest approach commensurate withthe requirements for the building. Although the Eurocodes only set out the general principlesassociated with advanced fire engineering methods, more detailed guidance is nowavailable.49

The minimum fire resistance requirements are defined in National regulations based on aconsideration of life safety of building occupants, those in the vicinity of the building and thefire service. Other issues such as property protection, protection of the environment andbusiness continuity are not considered. Therefore, in certain cases, a level of safety overand above that required by National regulations may be appropriate.

13.2. Guidance on selection of appropriate design methodThe hierarchy in terms of complexity of design methods is tabulated data followed by sim-plified calculation methods followed by advanced calculation methods. For the designer thetabulated approach should be the first port of call. This is particularly relevant in relation toconcrete and composite structures. Simplified calculation methods are appropriate for steeland composite buildings and concrete buildings where the dimensions or cover required donot meet the specified fire resistance period or where renovation of an existing structureinvolves a change of use resulting in a new fire resistance category being applied to the


building. Calculation methods can be used to demonstrate performance under specific con-ditions and may provide substantial savings (for example in applied passive fire protection tosteel structures) in certain circumstances. Advanced calculation methods (typically non-linear finite-element models) may be used where the structure is very complex and wherethe provisions of the National regulations are not applicable. Examples of such structureswould include sports stadia, exhibition halls and airport terminals.

122



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7. Office of the Deputy Prime Minister (2002) The Building Regulations 2000.Ammendments 2002 to Approved Document B. ODPM, London.

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REFERENCES


Index

Page numbers in italics refer to diagrams and illustrations.

adjacent members, indirect action 35�36advanced calculation methods 13advanced fire models

computational fluid dynamics 26

definitions 8use of 28

ambient temperatures, fire loads 37application rules, and principles, Eurocodes 5

atmospheric temperatures, external 26axis distance, definitions 8

beam-to-column, bolted joints 114�120, 114,115, 118, 119

blocked infilled steel columns 106, 107

bolted joints, beam-to-column 114�120, 114,115, 118, 119

bolts

fire resistance 55, 112strength reduction factors 55, 56, 113�114,

114box value of section factors, definitions 8

building materialsstandard time–temperature curves 20thermal properties 25

Building Regulationsfire resistance, UK 1�2traditional design methods 13

butt, welds, strength reduction factors 55�56,56

calculation methodsfire designadvanced 13simplified 13, 15, 16

tabulated data 13carbon steel (hot-rolled)

definitions 8

specific heat 40, 40stress–strain relationships 40�42, 42reduction factors 41�42, 42strain hardening 43, 43

thermal conductivity 41

thermal elongation 39�40, 40Cardington fire tests 111, 111CFD models see computational fluid dynamic

modelscold-formed light gauge steel see light gauge

steel (cold-formed)columns

compositeconcrete-filled hollow 78�79, 79design methods 67�70design tables 73�78partially encased 71�73, 71, 72

effective length, in fire 64, 64

reinforced concrete 63degree of utilization 38design methods 80�81fire resistance 37�38

steel 63with axial loads and bending moments

67

design methods 64�65, 65non-uniformly heated 67uniformly heated 65�67

combustion factors, definitions 8composite beamspartially encased

calculations 89�91, 90hogging moment resistance 89, 89stress distribution 88�89, 88

composite columnsconcrete-filled hollow 78�79, 79cross-sectional properties 68design methods 67�68, 69�70partially encased 71�73, 71, 72design tables 73�78loading eccentricity 78

resistance to axial compression 69temperatures in 68

composite joints, thermal gradients 112,

113


composite slabsdata 3

fire resistance 93load carrying capacity 94, 94in fire 96

fire resistance 94�95hogging moment resistance 95�96,

100�101, 101sagging moment resistance 95, 98�100thermal insulation 97�98using Annex D 96�97, 97

supports, slim floor beams 103, 104

unprotectedreinforcement bars 31�32, 31, 32slabs over steel decking 32�33, 32, 33steel decking 30�31

composite structures, fire resistance, verificationmethods 17�18

compression members see columnscomputational fluid dynamic (CFD) models

26

definitions 9concretedefinitions 48high-strength 53

temperature strength reduction 53, 54thermal properties 54

lightweight

moisture content 93specific heat 52stress–strain relationships 51, 51, 52�53thermal conductivity 50thermal elongation 52

normal-weight

calcareous aggregates 49density 50, 50moisture content 93siliceous aggregates 49

specific heat 49, 49stress–strain relationships 50�52, 51, 52thermal conductivity 50, 50

thermal strain/expansion 49, 49temperature reactions 2

concrete beams

reinforced, calculation methods 91temperature profiles 33, 34

concrete columnsreinforced

degree of utilization 38fire resistance 37�38

concrete connections

design 109�110thermal expansioneccentric deflections due to 110�111, 110moment distribution 110, 110restrained 110, 111

concrete slabs

expansion, curvature due to 110, 110over steel decking 32�33, 32temperature distribution 33, 33

reduced thickness5008C isotherm method 102

zone method 101�102supportsshelf angle beams 103�106, 104, 105, 106slim floor beams 103, 104

temperature profiles 33, 34concrete structures

see also composite structuresfire performance assessments 2fire provisions 3�4reinforcement, temperature rises 4

configuration factors, definitions 9connections see bolts; concrete connections;

joints; welds

construction materials see building materialsconvective heat transfer coefficients, definitions

9

critical temperature of reinforcement,definitions 9

critical temperatures of structural steel,

definitions 9

degree of utilization, reinforced concretecolumns 38

density, concrete, normal-weight 50, 50design fire load densities, definitions 9design fires, definitions 9

design proceduresEurocodes 13, 14, 15flexibility within 4, 121

selection of appropriate 121�122steel columns 64�65, 65steel structures 2

design values of loads 36�37

effective cross-sections, definitions 9effective yield strengths, definitions 9

emissivity, definitions 9equivalent time of fire exposure, definitions 9Eurocodes

definitions within 8�11design procedures 13, 14, 15flexibility within 4, 121

Nationally Determined Parameters 5�8principles, and application rules 5scope of 4�5

external atmospheric temperatures 26

external fire curves 20, 21definitions 9

external members, definitions 9

fillet welds, strength reduction factors 55�56,56

fire activation risks, definitions 9fire compartmentsdefinitions 9

and fire resistance 21gas temperatures 23�24

fire design resistance, bolts 55

128



fire design scenarioschoice of 19�20definitions 9, 19

fire exposuretime equivalence 21�22, 22calculation 22�23

fire limit statesfire loads 37

reduction factors 37fire load densities

by building type 26definitions 9

fire loadsambient temperatures 37definitions 9, 35

fire limit states 37indirect actions, adjacent members 35�36limit states 36�37uniformly distributed 37

fire modelsadvanced

definitions 8use of 28

simple, definitions 11fire performance assessments, concrete

structures 2fire protection

data 2�3moisture content 29�30, 29steelapplication 2�3passive 3thickness 3

fire protection materials, definitions 9

fire resistancebolts 55, 112composite slabs 93concrete columns, reinforced 37�38definitions 2, 10and fire compartments 21National regulations 1�2, 121periods, steel structures 2standard, definitions 11verification methods 15

welds 112fire scenarios, definitions 10fire spread

internal, requirements 2

restricting 3fire tests, standard 2fire walls, definitions 10

flash-over, definitions 10fully developed fires, definitions 10

gas temperatures, fire compartments 23�24global structural analysis, definitions 10

heat release, rate of, definitions 11high-strength concrete (HSC) 53

temperature strength reduction 53, 54

thermal properties 54hot-rolled carbon steel see carbon steel

(hot-rolled)hydrocarbon fire curves 20, 21definitions 10

indirect fire actions, definitions 10insulation, definitions 10

integrity, definitions 10internal fire spread, requirements 2

joints

beam-to-column, bolted 114�120, 114, 115,118, 119

bolts

fire resistance 55, 112strength reduction factors 55, 56, 113�114,

114

composite, thermal gradients 112, 113structural steelwork 111design 112

weldsfire resistance 112strength reduction factors 55�56, 56,

113�114, 113

light gauge steel (cold-formed)fire resistance 47

strength reduction factors 47�48, 48thermal properties 47uses 47

lightweight concrete (LWC)moisture content 93specific heat 52

stress–strain relationships 51, 51, 52�53thermal conductivity 50thermal elongation 52

load carrying capacity, composite slabs 94�101,94, 97, 99

load levels, reinforced concrete columns37�38

load ratio, definitions 3load-bearing functions, definitions 10localized fires, definitions 10

LWC see lightweight concrete

member analysis, definitions 10members, definitions 10

moisture contentconcretelightweight 93

normal-weight 93fire protection materials 29�30, 29

National regulations, fire resistance 1�2,121

Nationally Determined Parameters (NDP)

operation of 5�6summary of 6�8

net heat flux, definitions 10

129

INDEX


nominal temperature–time curves 21external 9, 20

hydrocarbon 11, 20standard 11, 20

normal temperature designs, definitions 10

normal-weight concrete (NWC)calcareous aggregates 49density 50, 50

moisture content 93siliceous aggregates 49specific heat 49, 49stress–strain relationships 50�52, 51, 52thermal conductivity 50, 50thermal strain/expansion 49, 49

one-zone models, definitions 10opening factors, definitions 11

parametric temperature-time curves 23�24,24

calculation 25�26and test results 24, 24

parts of structures, definitions 11prestressed reinforcement, temperature rises 4principles, and application rules, Eurocodes 5

protected members, definitions 11protective layers, definitions 11

rate of heat release, definitions 11reduced cross-sections, definitions 11reinforced concrete beams, calculation methods

91reinforced concrete columnsdegree of utilization 38

design methods5008C isotherm 80, 81zone 80�81, 80

fire resistance 37�38reinforcement barscritical temperatures 9prestressed, temperature rises 4

temperature rises 4unprotected, temperature determination

31�32, 31, 32reinforcing steelcold-rolled 54hot-rolled 54

section factors, definitions 11separating elements, definitions 11separating functions, definitions 11

shelf angle steel beams 103�104, 104temperature blocks 105�106, 105, 106

simple fire models, definitions 11

slender sections, calculation limitations 3slim floor steel beams 103, 104specific heat

concretelightweight 52normal-weight 49, 49

steelscarbon (hot-rolled) 40, 40

stainless 45, 45stainless steelsdefinitions 11

groups of 43specific heat 45, 45strain hardening 44

stress–strain relationships 45�46, 46reduction factors 45, 47

thermal conductivity 45thermal elongation 44, 44

thermal properties 44standard fire resistance, definitions 11standard fire tests 2

standard time–temperature curves 20, 21building materials 20definitions 11

steelsee also bolts; carbon steel (hot-rolled);

light-gauge steel (cold-formed);

reinforcing steel; stainless steels;welds

fire protectionapplication 2�3passive 3thickness 3

structural, critical temperatures 9

temperature reactions 2steel beamssee also composite beams

bending moment capacityassumed temperature distribution 84critical temperature method 85

plastic bending moment capacity method83�85

with concrete slab on fourth side 87�88deformation control 86�87lateral torsional bucklingnon-uniform temperature distribution

86

uniform temperature distribution 86shear resistance 85�86calculation 86

shelf angle 103�106, 104, 105, 106slim floor 103, 104

steel columns 63with axial loads and bending moments 67

blocked infilled 106, 107design methods 64�65, 65non-uniformly heated 67

uniformly heated 65�67steel deckingunprotected

concrete over 32�33, 32, 33, 87�88temperature determination 30�31

steel members

thermal responsesinsulated 28�30, 29unprotected 27�28, 28

130



steel structuressee also composite structures

designing 2fire resistanceperiods 2

verification methods 16�17strain hardening

carbon steel (hot-rolled) 43, 43

stainless steels 44stress–strain relationships

carbon steel (hot-rolled) 40�42, 42reduction factors 41�42, 42strain hardening 43, 43

concretelightweight 51, 51, 52�53normal-weight 50�52, 51, 52

stainless steels 45�46, 46reduction factors 45, 47

structural members, definitions 11structural steelwork

critical temperatures, definitions 9

joints 111design 112

structures, parts of, definitions 11

tabulated data, calculation methods 13temperature analysis, definitions 11temperature determination, steel decking,

unprotected 30�31temperature profiles

concrete beams 33, 34

concrete slabs 33, 34temperature reactions

concrete 2

steel 2temperature–time curves

parametric 23�24, 24calculation 25�26and test results 24, 24

standard 20building materials 20

definitions 11tension members

applications 57, 58

design resistance calculations 57�58critical temperature method 60�61

sections 57

temperature distributionsnon-uniform 58�60uniform 60

thermal actions, definitions 11thermal conductivity

concrete, normal-weight 50, 50steelscarbon (hot-rolled) 41

stainless 45thermal elongationconcretelightweight 52

normal-weight 49, 49steelscarbon (hot-rolled) 39�40, 40stainless 44, 44

thermal expansionconcrete connections

eccentric deflections due to 110�111, 110moment distribution 110, 110restrained 110, 111

steel membersinsulated 28�30, 29unprotected 27�28, 28

thermal exposure, assessment methods 19

thermal gradients, composite joints 112, 113thermal propertiesbuilding materials 25

steels, light gauge (cold-formed) 47time equivalencefire exposure 21�22, 22calculation 22�23

two-zone models, definitions 11

unprotected steel members, thermal responses27�28, 28

ventilation factors 21

weldsbutt, strength reduction factors 55�56, 56fillet, strength reduction factors 55�56, 56fire resistance 112strength reduction factors 55�56, 56,

113�114, 113

‘Yellow Book, The’, fire protection data 2�3

131

INDEX


Designers’ guide to EN1991-1-2, EN1992-1-2, EN1993-1-2

and EN1994-1-2T. Lennon, D. B. Moore, Y. C. Wang and C. G. Bailey

Series editor Haig Gulvanessian

This series of Designers’ Guides to the Eurocodes provides comprehensive guidance in the form of design aids, indications for the most convenient design procedures and worked examples. The books also include background information to aid the designer in understanding the reasoning behind and the objectives of the code. All individual guides work in conjunction with the Designers’ Guide to EN1990 Eurocode: Basis of structural design.

Designers’ Guide to EN1991-1-2, EN1992-1-2, EN1993-1-2 and EN1994-1-2 differs from the other Eurocode guides available in that it is not concerned with a single design standard. The UK standard for the design of steel structures encompasses the rules for both structural steelwork and for composite steel and concrete construction. The fire design procedures for reinforced and prestressed concrete structures are contained in the relevant part of the National code. However, the structural Eurocodes consider steel, composite and concrete construction in isolation and each material therefore has its own corresponding fire part.

The design methodology, as set out in the fire parts of the structural Eurocodes, is based on the principles adopted for normal temperature design. One of the aims of this book is to demystify the subject so that it can be readily understood and used by structural engineers used to the underlying principles and assumptions of design for the ambient condition. This present Designers’ Guide provides guidance on the nature of the loading that must first be understood before applying the structural engineering principles set out in the Eurocodes. For this reason the book is meant as a guide to four separate documents EN1991-1-2, EN1992-1-2, EN1993-1-2 and EN1994-1-2 with reference, where appropriate, to the Eurocode covering basis of design.

This guide is essential reading for:

■ civil and structural engineers■ code-drafting committees■ clients■ structural-design students■ public authorities

in fact, everyone who will be affected by the Eurocodes.

Tom Lennon has worked at the British Research Establishment for over 20 years. He was responsible for the programme of full-scale fire tests carried out at BRE’s large-scale test facility at Cardington on steel, concrete and timber framed buildings. Mr Lennon has extensive experience of the Structural Eurocodes. He is a prominent member of British Standards committee B525/-/32 the mirror group for the fire part of EC1 responsible for the implementation of the code in the UK. Mr Lennon is a member of the project team responsible for developing the draft National Annex for use with EN 1991-1-2. He is author of a number of papers, design guides and journal articles on the subject of structural fire engineering design.

Dr David B. Moore is the Director of Engineering at the British Constructional Steelwork Association and has over 25 years experience of research and specialist advisory work in the area of structural engineering and he has published over 50 technical papers on a wide range of subjects many of them in international journals. He has also made a significant contribution to a number of specialised design guides and best practice guides for the steel industry. Many of these publications are used daily by practising structural engineers and steelwork fabricators.

Dr Yong C. Wang teaches fire engineering at the University of Manchester and has been engaged in research on fire resistance of steel and composite structures for a number of years. He was Senior Research Engineer at the Building Research Establishment and was a member of the working group responsible for the amendment of BS5950 Part 8. He is the author of Steel and composite structures – behaviour and design for fire safety.

Colin G. Bailey is currently Professor of Structural Engineering at the University of Manchester. He has previously worked for the design consultants Lovell Construction, Cameron Taylor Bedford and Clarke Nicholls Marcel, where he designed and supervised the construction of a number of concrete, steel and masonry structures. He has also worked for The Steel Construction Institute and The Building Research Establishment, where his practical and research experience resulted in significant developments in structural engineering design. His main specialties are fire safety engineering of structures, membrane action, wind loading, and steel–concrete composite systems.





www.thomastelford.com/bookswww.eurocodes.co.uk

Designers’ G

uide to EN

1991-1-2, E

N1992-1-2, E

N1993-1-2 and E

N1994-1-2

Lennon, M

oore

, Wang &

Baile

y

Eurocode EN1991-1-2.indd 1Eurocode EN1991-1-2.indd 1 18/12/06 15:33:5318/12/06 15:33:53


designers guide to en 1991-1-2, en 1992-1-2, en 1993-1-2 and en 1994-1-2 handbook for the fire...

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